Question

In the given figure, a || b and c || d. If $\angle 1={75}^{\circ }$, what is the measure of $\angle 1$ + $\angle 2$ - $\angle 3$?

(3 marks)

Answer 1

Given a || b and c || d and $\angle 1={75}^{\circ }$
Since, a || b,
$\angle 1=\angle 2={75}^{\circ }$ (corresponding angles are equal)
(0.5 mark)

Also c || d,
$\Rightarrow \angle 2+\angle 3={180}^{\circ }\left[\text{sum of co-interior angles is 180}\right]$
(1 mark)

$\therefore \angle 3={180}^{\circ }-{75}^{\circ }={105}^{\circ }$
(0.5 mark)

Hence, the value of $\angle 1$ + $\angle 2$ - $\angle 3$ = 45⁰
(1 mark)