Question

If $m\angle 1=130$what are the measures of the other numbered angels?

Short answer

Measures of numbered angles are

$\mathit{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{50}\mathbf{;}\mathit{m}\mathbf{\angle }\mathbf{3}\mathbf{=}\mathbf{50}\mathbf{;}\mathit{m}\mathbf{\angle }\mathbf{4}\mathbf{=}\mathbf{130}\mathbf{;}\mathit{m}\mathbf{\angle }\mathbf{5}\mathbf{=}\mathbf{130}\mathbf{;}\mathit{m}\mathbf{\angle }\mathbf{6}\mathbf{=}\mathbf{50}\mathbf{;}\mathit{m}\mathbf{\angle }\mathbf{7}\mathbf{=}\mathbf{50};\text{and}\mathit{m}\mathbf{\angle }\mathbf{8}\mathbf{=}\mathbf{13}0$

Step-by-step solution

Step 1. Observations from figure

• Arrowheads are shown on lines $I$and $P$, so these lines are parallel
• Line $t$is transversal to the parallel lines $I$and$P$

Step 2. Find m angle 2

$\angle 1$and $\angle 2$forms linear pair, so sum of these angles is 180

$\begin{array}{c}m\angle 1+m\angle 2=180\\ 130+m\angle 2=180\end{array}$

$m\angle 2=180-130$

Step 3. Find m angle 3

$\angle 2$ and $\angle 3$are vertically opposite angles, so there values are equal

$m\angle 3=m\angle 2$

Thus,$m\angle 3=50$

Step 4. Find m angle 4

$\angle 1$and $\angle 4$are vertically opposite angles, so there values are equal

$m\angle 4=m\angle 1$

Thus,$m\angle 4=130$

Step 5. Find m angle 5, m angle 6, m angle 7, and m angle 8

Since, corresponding angles are equal

Pair of corresponding angles are

$\left(\angle 1-\angle 5\right),\left(\angle 2-\angle 6\right),\left(\angle 3-\angle 7\right),\text{and}\left(\angle 4-\angle 8\right)$

Thus, measurement of these angles are

$\begin{array}{c}m\angle 5=130\\ m\angle 6=50\\ m\angle 7=50\\ m\angle 8=130\end{array}$