Question

Find the value of x in the below diagram.
[4 MARKS]
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Answer 1

Properties : 1 Mark
Steps : 2 Marks
Result : 1 Mark

According to the question, Sides AB and AC are equal and $\angle B$ is a right-angled triangle.

Let $\angle A$ be y, then $\angle ACB$ will also be y ($\because$ equal sides have equal angles)
In any triangle, Sum of all angles = 180${}^o$
Or, y + y + 90${}^o$ = 180${}^o$
Or, 2y = 180${}^o$ - 90${}^o$
Or, y = $\frac{{90}^o}{2}$ = 45${}^o$

X here is an exterior angle to $\angle A$ and $\angle B$
Sum of interior angles = exterior angle.
Or, y + 90${}^o$ = X
Or, X = 90${}^o$ + 45${}^o$ = 135${}^o$