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Angles on a line, around a point, and inside triangles and quadrilaterals.
Question 1 of 12
Three angles in a quadrilateral are 97°, 95° and 56°. What is the remaining angle?
The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 97 + 95 + 56 = 248°, so the last one is 360 − 248 = 112°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. Angles in a triangle come to 180°, in a quadrilateral 360°. Learn both; papers use them equally.
The answer is D. The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 97 + 95 + 56 = 248°, so the last one is 360 − 248 = 112°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. Angles in a triangle come to 180°, in a quadrilateral 360°. Learn both; papers use them equally.
Four angles meet at a point. Three of them are 53°, 107°, 53°. What is the fourth angle?
Angles around a point add up to 360°, because that is a full turn. The angles given come to 53 + 107 + 53 = 213°. 360 − 213 = 147°. Checking: 53 + 107 + 53 + 147 = 360°. A straight line is 180°, a full turn is 360°, and a right angle is 90°. Those three facts answer most angle questions in a KS2 paper.
The answer is C. Angles around a point add up to 360°, because that is a full turn. The angles given come to 53 + 107 + 53 = 213°. 360 − 213 = 147°. Checking: 53 + 107 + 53 + 147 = 360°. A straight line is 180°, a full turn is 360°, and a right angle is 90°. Those three facts answer most angle questions in a KS2 paper.
Four angles meet at a point. Three of them are 65°, 88°, 66°. What is the fourth angle?
Angles around a point add up to 360°, because that is a full turn. The angles given come to 65 + 88 + 66 = 219°. 360 − 219 = 141°. Checking: 65 + 88 + 66 + 141 = 360°. A straight line is 180°, a full turn is 360°, and a right angle is 90°. Those three facts answer most angle questions in a KS2 paper.
The answer is B. Angles around a point add up to 360°, because that is a full turn. The angles given come to 65 + 88 + 66 = 219°. 360 − 219 = 141°. Checking: 65 + 88 + 66 + 141 = 360°. A straight line is 180°, a full turn is 360°, and a right angle is 90°. Those three facts answer most angle questions in a KS2 paper.
Two angles in a triangle are 67° and 59°. What is the remaining angle?
The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 67 + 59 = 126°, so the last one is 180 − 126 = 54°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. Add the known angles first, then subtract from the total.
The answer is B. The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 67 + 59 = 126°, so the last one is 180 − 126 = 54°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. Add the known angles first, then subtract from the total.
Two angles in a triangle are 64° and 29°. What is the remaining angle?
The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 64 + 29 = 93°, so the last one is 180 − 93 = 87°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. Angles in a triangle come to 180°, in a quadrilateral 360°. Learn both; papers use them equally.
The answer is D. The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 64 + 29 = 93°, so the last one is 180 − 93 = 87°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. Angles in a triangle come to 180°, in a quadrilateral 360°. Learn both; papers use them equally.
Three angles sit on a straight line. Two of them are 32° and 47°. What is the third angle?
Angles on a straight line add up to 180°, because that is a half turn. The angles given come to 32 + 47 = 79°. 180 − 79 = 101°. Checking: 32 + 47 + 101 = 180°. Add what you have been given first, then take it from the total. Doing it the other way round is slower and no safer.
The answer is C. Angles on a straight line add up to 180°, because that is a half turn. The angles given come to 32 + 47 = 79°. 180 − 79 = 101°. Checking: 32 + 47 + 101 = 180°. Add what you have been given first, then take it from the total. Doing it the other way round is slower and no safer.
Two angles in a triangle are 78° and 27°. What is the remaining angle?
The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 78 + 27 = 105°, so the last one is 180 − 105 = 75°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. If the answer comes out negative or over the total, one of the given angles has been misread.
The answer is D. The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 78 + 27 = 105°, so the last one is 180 − 105 = 75°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. If the answer comes out negative or over the total, one of the given angles has been misread.
Two angles in a triangle are 68° and 28°. What is the remaining angle?
The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 68 + 28 = 96°, so the last one is 180 − 96 = 84°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. If the answer comes out negative or over the total, one of the given angles has been misread.
The answer is D. The angles in a triangle always add up to 180°, whatever its shape. The angles given come to 68 + 28 = 96°, so the last one is 180 − 96 = 84°. Tearing the three corners off a paper triangle and laying them side by side makes a straight line — that is the 180°. If the answer comes out negative or over the total, one of the given angles has been misread.
Three angles sit on a straight line. Two of them are 50° and 54°. What is the third angle?
Angles on a straight line add up to 180°, because that is a half turn. The angles given come to 50 + 54 = 104°. 180 − 104 = 76°. Checking: 50 + 54 + 76 = 180°. A straight line is 180°, a full turn is 360°, and a right angle is 90°. Those three facts answer most angle questions in a KS2 paper.
The answer is D. Angles on a straight line add up to 180°, because that is a half turn. The angles given come to 50 + 54 = 104°. 180 − 104 = 76°. Checking: 50 + 54 + 76 = 180°. A straight line is 180°, a full turn is 360°, and a right angle is 90°. Those three facts answer most angle questions in a KS2 paper.
Three angles sit on a straight line. Two of them are 45° and 55°. What is the third angle?
Angles on a straight line add up to 180°, because that is a half turn. The angles given come to 45 + 55 = 100°. 180 − 100 = 80°. Checking: 45 + 55 + 80 = 180°. Add what you have been given first, then take it from the total. Doing it the other way round is slower and no safer.
The answer is A. Angles on a straight line add up to 180°, because that is a half turn. The angles given come to 45 + 55 = 100°. 180 − 100 = 80°. Checking: 45 + 55 + 80 = 180°. Add what you have been given first, then take it from the total. Doing it the other way round is slower and no safer.
Three angles in a quadrilateral are 62°, 98° and 91°. What is the remaining angle?
The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 62 + 98 + 91 = 251°, so the last one is 360 − 251 = 109°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. Add the known angles first, then subtract from the total.
The answer is D. The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 62 + 98 + 91 = 251°, so the last one is 360 − 251 = 109°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. Add the known angles first, then subtract from the total.
Three angles in a quadrilateral are 104°, 65° and 71°. What is the remaining angle?
The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 104 + 65 + 71 = 240°, so the last one is 360 − 240 = 120°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. Add the known angles first, then subtract from the total.
The answer is B. The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 104 + 65 + 71 = 240°, so the last one is 360 − 240 = 120°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. Add the known angles first, then subtract from the total.
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