Angle Properties — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Sum of interior angles = (n−2)×180° with n=6, then divide by 6 for a regular polygon.

(6−2)×180 = 720°; each angle = 720 ÷ 6 = 120°

Question 2

(a)Exterior angles of any polygon sum to 360°; for a regular polygon divide by the number of sides.

360 ÷ 5 = 72°

Question 3

(a)Sum = (n−2)×180° with n=8, then divide by 8 for a regular polygon.

(8−2)×180 = 1080°; each = 1080÷8 = 135°

Question 4

(a)Exterior angles of a regular polygon = 360° ÷ number of sides.

360 ÷ 10 = 36°

Question 5

(a)Angles in a triangle sum to 180°.

180 − 50 − 65 = 65°

Question 6

(a)Co-interior (allied) angles lie between the parallel lines on the same side of the transversal, and are supplementary.

Co-interior angles sum to 180°

Question 7

(a)Angles in a quadrilateral sum to 360°.

360 − 90 − 85 − 100 = 85°

Question 8

(a)Interior angle = (n−2)×180°/n.

(9−2)×180 ÷ 9 = 140°

Question 9

(a)Vertically opposite angles are formed where two lines cross.

They are always equal

Question 10

(a)Alternate angles are formed on opposite sides of the transversal, between the parallel lines.

They are always equal

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