Question

Find the value of x in the following 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 BC are equal and $\angle B$ is 90°

Let $\angle A$ be y, then $\angle ACB$ will also be y ($\because$ angle opposite to the equal sides are equal)
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 opposite interior angles = exterior angle.
Or, y + 90${}^o$ = X
Or, X = 90${}^o$ +45${}^o$ = 135${}^o$