Question

use the diagram and the given angle measure to find the other three measures. m∠4 = 29° m∠1 = ° m∠2 = ° m∠3 = °

Explanation:

Step1: Vertical - angles are equal

$\angle1$ and $\angle3$ are vertical - angles with $\angle4$. Since vertical angles are equal, $m\angle1 = m\angle3$. Given $m\angle4=29^{\circ}$, then $m\angle1 = 29^{\circ}$ and $m\angle3 = 29^{\circ}$.

Step2: Supplementary - angles sum to 180°

$\angle2$ and $\angle4$ are supplementary angles (they form a linear pair). So $m\angle2 + m\angle4=180^{\circ}$. Then $m\angle2=180 - m\angle4$. Substituting $m\angle4 = 29^{\circ}$, we get $m\angle2=180 - 29=151^{\circ}$.

Answer:

$m\angle1 = 29^{\circ}$
$m\angle2 = 151^{\circ}$
$m\angle3 = 29^{\circ}$