Question

Find the measures of the angle marked by the letters in the following diagram,

Answer 1

Given :

In the given diagram, $\mathrm{q}$ is the exterior angle of the triangle whose two opposite interior angles are $88°$ and $27°$.

And, $\mathrm{p}$ is the exterior angle of the triangle whose two opposite interior angles are $20°$ and $\mathrm{q}$.

Since, Exterior angle is equal to the sum of two interior opposite angles.

$$\begin{gathered} \therefore \mathrm{q}=88+27 \\ =115° \end{gathered}$$

Similarly, $\mathrm{p}=20+\mathrm{q}$

$=20+115$

$=135°$

Hence, the value of $\mathrm{q}=115°\text{and}\mathrm{p}=135°$.