91Ó°ÊÓ

The Angle addition postulate states that if two angles are placed side by side, then the value of the resulting angle is equal to the sum of the original angles.

From the above figure it can be observe that $\stackrel{→}{a}$and $\stackrel{→}{b}$both represents straight angles, therefore, resulting in following equations:

$$\begin{gathered} m∠1+m∠2=180°………\left(1\right) \\ m∠1+m∠4=180°………\left(2\right) \\ m∠3+m∠4=180°………\left(3\right) \end{gathered}$$

In order to calculate $m∠2$, substitute $t$for $m∠1$into the equation (1) $m∠1+m∠2=180°$.

localid="1649244753263" role="math" $$\begin{gathered} t+m∠2=180° \\ m∠2=180°-t \end{gathered}$$

In order to calculate $m∠4$, substitute $t$for $m∠1$into the equation (2) $m∠1+m∠4=180°$.

role="math" localid="1649244728985" $$\begin{gathered} m∠1+m∠4=180° \\ t+m∠4=180° \\ m∠4=180°-t \end{gathered}$$

In order to calculate $m∠3$, substitute $180°-t$for $m∠4$into the equation (2) $m∠3+m∠4=180°$.

$$\begin{gathered} m∠3+m∠4=180° \\ m∠3+180°-t=180° \\ m∠3=180°-180°+t \\ m∠3=t \end{gathered}$$

Therefore, themeasure of the angles is$m∠2=180°-t$,$m∠3=t$and$m∠4=180°-t$.