Question

pls help me to find x and y​

Answer 1

★ How to do :-

Here, we are given with five triangles which are consisting of an exterior angle each. There are two variables in each triangle. We should find the value of each angle in that triangle. So, we are going to use the concepts of linear pair of angles, sum of all angles in triangle. So, lets do!!

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➤ Solution (1) :-

Value of ∠y :-

${\tt \leadsto 180 = 100 + y}$

${\tt \leadsto y = 180 - 100}$

${\tt \leadsto \orange{\boxed{\tt y = {80}^{\circ}}}}$

Value of ∠x :-

${\tt \leadsto 180 = (180 - 125) + 80 + x}$

${\tt \leadsto 180 = 55 + 80 + x}$

${\tt \leadsto 180 = 135 + x}$

${\tt \leadsto x = 180 - 135}$

${\tt \leadsto \orange{\boxed{\tt x = {45}^{\circ}}}}$

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➤ Solution (2) :-

Value of ∠y :-

${\tt \leadsto 180 = 120 + y}$

${\tt \leadsto y = 180 - 120}$

${\tt \leadsto \orange{\boxed{\tt y = {60}^{\circ}}}}$

Value of x :-

${\tt \leadsto 180 = 60 + x + (x + 20)}$

${\tt \leadsto 180 = 60 + 2x + 20}$

${\tt \leadsto 180 = 80 + 2x}$

${\tt \leadsto 2x = 180 - 80}$

${\tt \leadsto 2x = 100}$

${\tt \leadsto x = \cancel \dfrac{100}{2} = 50}$

${\tt \leadsto \orange{\boxed{\tt x = {50}^{\circ}}}}$

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➤ Solution (3) :-

Value of ∠y :-

${\tt \leadsto 180 = 150 + y}$

${\tt \leadsto y = 180 - 150}$

${\tt \leadsto \orange{\boxed{\tt y = {30}^{\circ}}}}$

Value of x :-

${\tt \leadsto 180 = 30 + 2x + 3x}$

${\tt \leadsto 180 = 30 + 5x}$

${\tt \leadsto 5x = 180 - 30}$

${\tt \leadsto 5x = 150}$

${\tt \leadsto x = \cancel \dfrac{150}{5} = 30}$

${\tt \leadsto \orange{\boxed{\tt x = {30}^{\circ}}}}$

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➤ Solution (4) :-

Value of ∠x :-

${\tt \leadsto 180 = 130 + x}$

${\tt \leadsto x = 180 - 130}$

${\tt \leadsto \orange{\boxed{\tt x = {50}^{\circ}}}}$

Value of ∠y :-

${\tt \leadsto 180 = 50 + (180 - 110) + y}$

${\tt \leadsto 180 = 50 + 70 + y}$

${\tt \leadsto 180 = 120 + y}$

${\tt \leadsto y = 180 - 120}$

${\tt \leadsto \orange{\boxed{\tt y = {60}^{\circ}}}}$

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➤ Solution (5) :-

Value of ∠x :-

${\tt \leadsto 180 = 116 + x}$

${\tt \leadsto x = 180 - 116}$

${\tt \leadsto \orange{\boxed{\tt x = {64}^{\circ}}}}$

Value of ∠y :-

${\tt \leadsto 180 = 64 + y + y}$

${\tt \leadsto 180 = 64 + 2y}$

${\tt \leadsto 2y = 180 - 64}$

${\tt \leadsto 2y = 116}$

${\tt \leadsto y = \cancel \dfrac{116}{2} = 58}$

${\tt \leadsto \orange{\boxed{\tt y = {58}^{\circ}}}}$