Problem 1 : Show In triangle PQR, the measure of ∠P is 36. The measure of ∠Q is five times the measure of ∠R. Find ∠Q and ∠R. Solution : ∠P = 36 ∠Q = 5∠R In triangle PQR, the sum of interior angles is 180°. ∠P + ∠Q + ∠R = 180° 36° + 5∠R + ∠R = 180° 6R + 36° = 180° Subtract 36° from both sides. 6∠R = 144° Divide both sides by 6. ∠R = 24° ∠Q = 5∠R ∠Q = 5(24°) ∠Q = 120° Problem 2 : The exterior angle of a triangle is 120°. Find the value of x if the opposite non-adjacent interior angles are (4x + 40)° and 60°. Solution : Using Exterior Angle Theorem, (4x + 40)° + 60° = 120° 4x + 40 + 60 = 120 4x + 100 = 120 Subtract 100 from both sides. 4x = 20 Divide both sides by 4. 5 = x Problem 3 : Find the values of x, y and z. Solution : x° + z° = 56° ----(1) y° and 56° are linear pair. y° + 56° = 180° Subtract 56 from both sides. y = 124 x° and 144° are linear pair. x° + 144° = 180° Subtract 144 from both sides. x = 36 Substitute x = 36 in (1). 36 + z = 56 Subtract 36 from both sides. z = 20 Problem 4 : Find the values of x, y and z. Solution : Using Exterior Angle Theorem, y° = 26° + 26° y = 52 By Angle Sum Property of Triangle, x° + y° + 64° = 180° X + 52 + 64 = 180 x + 116 = 180 Subtract 116 from both sides. x = 64 Problem 5 : Solution : Using Exterior Angle Theorem, x° + 33° = z° x + 33 = z ----(1) z° and 133° are linear pair. z + 133 = 180 Subtract 133 from both sides. z = 47 Substitute z = 47 in (1). x + 33 = 47 Subtract 33 from both sides. x = 14 By Angle Sum Property of Triangle, y° + z° +114° = 180° y + z + 114 = 180 Subtract 114 from both sides. y + z = 66 Substitute z = 47. y + 47 = 66 y = 19 Problem 6 : Find the values of i and n. Solution : Vertically opposite angles are equal. Using Exterior Angle Theorem, n° = 114° + 33° n = 147 By Angle Sum Property of Triangle, 94° + i° + 33° = 180° i + 127 = 180 Subtract 127 from both sides. i = 53 Kindly mail your feedback to We always appreciate your feedback. ©All rights reserved. onlinemath4all.com How do you find the interior and exterior angles of a triangle?How do I find interior and exterior angles of a triangle? To find an interior angle of a triangle, take the sum two known interior angles of a triangle and subtract the number from 180. To find an exterior angle of a triangle, simply calculate the sum two opposite interior angles of a triangle.
What is exterior of a triangle class 7?An exterior angle of a triangle is equal to the sum of its interior opposite angles. For ΔABC,∠ACD, is an exterior angle. ∠ABC, ∠BACareinterior opposite angles. We know, an exterior angle of a triangle is equal to the sum of its interior opposite angles.
What is the interior angle of triangle?60° (for equilateral)Triangle / Internal anglenull
What is the sum of the exterior angles of a triangle?So, the sum of the exterior angles of a triangle is 360°.
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