Question

Find the size of the each of the angle marked with the letter in the diagram.Equal sides are marked by the dashes and parallel sides are marked by double arrows.

Answer 1

Step 1 : Since sum of all angles of triangle is $180°$

$$\begin{gathered} \Rightarrow 38°+60°+\angle x=180° \\ \Rightarrow 98°+\angle x=180° \\ \Rightarrow \angle x=180°-98° \\ \therefore \angle x=82° \end{gathered}$$

Step 2 : We know that “Exterior angle is equal to sum of two interior opposite angles”

$$\begin{gathered} \therefore 28°+\angle z=82° \\ \Rightarrow \angle z=82°-28° \\ \Rightarrow \angle z=54° \end{gathered}$$

Again,

$\angle y=38°+60°=98°$ (Exterior angle is equal to sum of two interior opposite angles)

$\Rightarrow \angle y=98°$

Hence, the required value if angles are $\angle x=82°,\angle y=98°\text{and}\angle z=54°$