Question

If $\mathbf{m}\angle \mathbf{1}\mathbf{=}\mathbf{30}$and $\mathbf{m}\angle \mathbf{4}\mathbf{=}\mathbf{130}$ then$\mathbf{m}\angle \mathbf{2}\mathbf{=}\mathbf{?}$

Short answer

The measure of$\angle 2$ is 100.

Step-by-step solution

Step 1. Highlight ∠1, ∠2 and ∠4.

Step 2. Apply exterior angle theorem.

The measure of an exterior angle is equal to the sum of measure of two remote interior angles.

Step 3. Description of step.

From the figure it can be observed that$\angle 1,\angle 2$ are remote interior angles$\angle 4$and is exterior angle then by exterior angle theorem,

$$\begin{gathered} m\angle 1+m\angle 2=m\angle 4 \\ 30+m\angle 2=130 \\ m\angle 2=130-30 \\ =100 \end{gathered}$$

Therefore, the measure of$\angle 2$ is 100.