Question

In the given figures, find the measures of angles x and y.​

Answer 1

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$\longrightarrow \rm \: AB = BC \\ \\ \rm \: so \\ \\ \rm\angle BAC \: = \angle ACB = x$

$\star \rm \: \: in \: \triangle \: ABC \: \\ \\ \rm \implies\: x + x + 90 \degree = 180 \degree \\ \\ \rm \implies \: 2x = 90 \degree \\ \\ \rm \implies \: \boxed{ \pink {x = 45 \degree}}$

$\rm \: as \: BC \: is \: a \: straight \: line$

$\implies \: \rm \angle ACB + y = 180 \degree \\ \\ \rm \implies \: x + y = 180 \degree \\ \\ \rm \implies \: 45 \degree + y = 180 \degree \\ \\ \rm \implies \: \boxed{ \pink{y = 135 \degree}}$

Answer 2

Answer:

Step by step instructions:

B=45°

AB=BC

Angle A= Angle C [In a ∆ angles opposite to equal angles are equal]

In ∆ABC

A+B+C=180°

X+90°+X=180° [A=C=X]

2X=90°

X=90°/2=45°

Therefore, Angle A = Angle C = 45°

now, exterior Angle C + Angle C = 180°[Linear Pair]

Y+45°=180°

Y=135°

Therefore, X=45° and Y=135°