In △ A B C , A B = A C , ∠ A = ( 5 x + 20 ) ° and each of the base angle is 2 5 th of ∠ A . Find ∠ A .

Given, in ∆ A B C , A B = A C , ∠ A = 5 x + 20 ° The sum of the angles in a triangle is 180 ° . ∠ A + ∠ B + ∠ C = 180 ° ⇒ 5 x + 20 + 2 5 ( 5 x + 20 ) + 2 5 ( 5 x + 20 ) = 180 ° ⇒ 5 x + 20 + 4 5 ( 5 x + 20 ) = 180 ⇒ 25 x + 100 + 20 x + 80 = 900 ⇒ 45 x = 900 - 180 ⇒ 45 x = 720 ⇒ x = 720 45 = 16 ∴ ∠ A = 5 x + 20 ⇒ ∠ A = 5 ( 16 ) + 20 ⇒ ∠ A = 80 + 20 ⇒ ∠ A = 100 ° Thus, ∠ A is equal to 100 ° .

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Mathematics>Chapter 4 - Geometry>TEST YOUR SKILLS>Q 3

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In the adjoining figure, $∠ A = ∠ D = 90 °$ , $∠ C = 48 °$ . $B E$ bisector of $∠ B$ , $A D$ and $B E$ intersect at $M$ . Calculate $∠ B M D$ .

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Mathematics>Chapter 4 - Geometry>TEST YOUR SKILLS>Q 3

In the adjoining figure, $∠ A = ∠ D = 90 °$ , $∠ C = 48 °$ $\Rightarrow ∠ B M D = 69 °$ bisector of $∠ B$ . $A D$ and $B E$ intersect at $M$ . Calculate $∠ A M E$ .

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Mathematics>Chapter 4 - Geometry>TEST YOUR SKILLS>Q 3

In the given figure, $∠ A = ∠ D = 90 °$ , $∠ C = 48 °$ . $B E$ is bisector of $∠ B$ , $A D$ and $B E$ intersect at $M$ . Calculate prove that $A E = A M$ .