In the given figure, x : y = 2 : 3 and ∠ A C D = 130 ∘ . Find the values of x , y and z .

Given, x : y = 2 : 3 and ∠ A C D = 130 ∘ . x y = 2 3 ⇒ 3 x = 2 y ⇒ x = 2 3 y We know that, the exterior angle of a triangle is equal to the sum of the interior opposite angles. ∠ A B C + ∠ B A C = ∠ A C D ⇒ x + y = 130 ∘ ⇒ 2 y 3 + y = 130 ∘ ⇒ 2 y + 3 y 3 = 130 ∘ ⇒ 5 y = 130 ∘ × 3 ⇒ 5 y = 390 ∘ ⇒ y = 78 ∘ ⇒ x = 2 3 × 78 ∘ ⇒ x = 52 ∘ We know that, angle sum property of triangle states that the sum of interior angles of a triangle is 180 ∘ . Therefore, x + y + z = 180 ∘ ⇒ 52 ° + 78 ° + z = 180 ° ⇒ z = 180 ° - 130 ° ⇒ z = 50 ° Hence, x ∘ = 52 ∘ , y ∘ = 78 ∘ and z ∘ = 50 ∘ .

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MATHEMATICS FOR CLASS 7>Chapter 15 - Properties of Triangles>EXERCISE 15B

R S Aggarwal Solutions for Chapter: Properties of Triangles, Exercise 2: EXERCISE 15B

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Chapter: Properties of Triangles, Exercise 2: EXERCISE 15B

Attempt the practice questions on Chapter 15: Properties of Triangles, Exercise 2: EXERCISE 15B with hints and solutions to strengthen your understanding. MATHEMATICS FOR CLASS 7 solutions are prepared by Experienced Embibe Experts.