Question

example 1: find the measure of each angle. find m∠1, m∠2, and m∠3 if m∠4 = 110°. m∠1 = 70 m∠2 = __ m∠3 = __ ∠1+∠4 = 180 ∠1 + 110 = 180 - 110 - 110 ∠1 = 70 ∠2

Explanation:

Step1: Use linear - pair property

$\angle1$ and $\angle4$ form a linear pair. So, $m\angle1 + m\angle4=180^{\circ}$. Given $m\angle4 = 110^{\circ}$, then $m\angle1=180 - 110=70^{\circ}$.

Step2: Use vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal. So, $m\angle2=m\angle4 = 110^{\circ}$.

Step3: Use vertical - angle property

$\angle3$ and $\angle1$ are vertical angles. Vertical angles are equal. So, $m\angle3=m\angle1 = 70^{\circ}$.

Answer:

$m\angle1 = 70^{\circ}$, $m\angle2 = 110^{\circ}$, $m\angle3 = 70^{\circ}$