Question

Write the measure of every marked with '?' in the figures below:

(1)

(2)

(3)

(4)

Answer 1

(1) ∵ $\angle SWP$ = 90°
∴ $\angle JWP$ + $\angle JWS$ = 90°
= 37° + $\angle JWS$ = 90°
= $\angle JWS$ = 90° – 37°
= $\angle JWS$ = 53°

(2) $\angle JGF$ and $\angle JGH$ form a linear pair.
The sum of the measures of such angles is 180°.
∴ $\angle JGF$ + $\angle JGH$ = 180°
= 110° + $\angle JGH$ = 180°
= $\angle JGH$ = 180° – 110°
= $\angle JGH$= 70°

(3) $\angle WYZ$ and $\angle WYX$ form a linear pair.
The sum of the measures of such angles is 180°.
∴ $\angle WYZ$ + $\angle WYX$ = 180°
= 132° + $\angle WYX$ = 180°
= $\angle WYX$ = 180° – 132°
= $\angle WYX$ = 48°

(4) ∵ $\angle QOR$ = 90°
∴ $\angle QOP$ + $\angle POR$ = 90°
= 45° + $\angle POR$ = 90°
= $\angle POR$ = 90° – 45°
= $\angle POR$ = 45°