Question

Find the value of $\angle C$ in the triangle given below if the value of $\angle CAB$ = 25${}^o$. If AB = BD, what can be the value of $\angle D$? [3 MARKS]

Answer 1

Steps: 1 Mark
Solution for $\angle C$ and $\angle D$: 2 Marks

In the given triangle CAB
Sum of opposite interior angles = exterior angle
Or, $\angle C$ + $\angle CAB$ = 90${}^o$
Or, $\angle C$ = 90${}^o$ - 25${}^o$
Or, $\angle C$ = 65${}^o$

$\because$ AB = BD $\Rightarrow \angle BAD=\angle D=y\left(say\right)$ (Equal sides have equal angles opposite to them.)
$\Rightarrow \angle BAD+\angle D+90=180$
$\Rightarrow \angle BAD+\angle D=90$
$\Rightarrow 2y=90$
$\because \angle BAD=\angle D=y$
$\Rightarrow y=\frac{90}{2}$
$\Rightarrow y=45$

$\therefore \angle BAD=\angle D={45}^{\circ }$