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Angles on a line, around a point, and inside triangles and quadrilaterals.
Question 1 of 12
Four angles meet at a point. Three of them are 65°, 46°, 57°. 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 + 46 + 57 = 168°. 360 − 168 = 192°. Checking: 65 + 46 + 57 + 192 = 360°. Sense-check against a right angle: does the answer look bigger or smaller than 90°?
The answer is D. Angles around a point add up to 360°, because that is a full turn. The angles given come to 65 + 46 + 57 = 168°. 360 − 168 = 192°. Checking: 65 + 46 + 57 + 192 = 360°. Sense-check against a right angle: does the answer look bigger or smaller than 90°?
Three angles sit on a straight line. Two of them are 80° and 67°. 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 80 + 67 = 147°. 180 − 147 = 33°. Checking: 80 + 67 + 33 = 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 80 + 67 = 147°. 180 − 147 = 33°. Checking: 80 + 67 + 33 = 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.
Four angles meet at a point. Three of them are 62°, 90°, 36°. What is the fourth angle?
Angles around a point add up to 360°, because that is a full turn. The angles given come to 62 + 90 + 36 = 188°. 360 − 188 = 172°. Checking: 62 + 90 + 36 + 172 = 360°. Sense-check against a right angle: does the answer look bigger or smaller than 90°?
The answer is D. Angles around a point add up to 360°, because that is a full turn. The angles given come to 62 + 90 + 36 = 188°. 360 − 188 = 172°. Checking: 62 + 90 + 36 + 172 = 360°. Sense-check against a right angle: does the answer look bigger or smaller than 90°?
Three angles in a quadrilateral are 75°, 88° and 70°. What is the remaining angle?
The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 75 + 88 + 70 = 233°, so the last one is 360 − 233 = 127°. 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 75 + 88 + 70 = 233°, so the last one is 360 − 233 = 127°. 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 sit on a straight line. Two of them are 50° and 33°. 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 + 33 = 83°. 180 − 83 = 97°. Checking: 50 + 33 + 97 = 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 + 33 = 83°. 180 − 83 = 97°. Checking: 50 + 33 + 97 = 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.
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.
Three angles in a quadrilateral are 109°, 58° and 93°. What is the remaining angle?
The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 109 + 58 + 93 = 260°, so the last one is 360 − 260 = 100°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. If the answer comes out negative or over the total, one of the given angles has been misread.
The answer is B. The angles in a quadrilateral always add up to 360°, whatever its shape. The angles given come to 109 + 58 + 93 = 260°, so the last one is 360 − 260 = 100°. A quadrilateral is two triangles joined along a diagonal, which is where the 360° comes from. 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 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 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 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.
Four angles meet at a point. Three of them are 78°, 100°, 54°. What is the fourth angle?
Angles around a point add up to 360°, because that is a full turn. The angles given come to 78 + 100 + 54 = 232°. 360 − 232 = 128°. Checking: 78 + 100 + 54 + 128 = 360°. Sense-check against a right angle: does the answer look bigger or smaller than 90°?
The answer is C. Angles around a point add up to 360°, because that is a full turn. The angles given come to 78 + 100 + 54 = 232°. 360 − 232 = 128°. Checking: 78 + 100 + 54 + 128 = 360°. Sense-check against a right angle: does the answer look bigger or smaller than 90°?
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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