Question

Find the measures of angle marked by the letters in the following diagram.parallel lines are marked by double arrows

Answer 1

Step 1 : Exterior angle is equal to sum of two interior angle

$$\begin{gathered} \Rightarrow \angle a+90°=120° \\ \Rightarrow \angle a={120}^{\circ }-{90}^{\circ } \\ \therefore \angle a=30° \end{gathered}$$

Similarly,

$$\begin{gathered} \Rightarrow \angle d+28°=90° \\ \Rightarrow \angle d=90°-28° \\ \therefore \angle d=62 \end{gathered}$$

Step 2 : Since angles on straight line is $180°$

$$\begin{gathered} \Rightarrow 62°+\angle b+30°=180° \\ \Rightarrow \angle b=180-92° \\ \therefore \angle b=88 \end{gathered}$$°

Hence, the required angles are $\angle a=30°,\angle b=88°$