Question

1. given the diagram below, the m∠2 is 86°. find and m∠4, m∠6, m∠7 and m∠5. m∠4= degrees m∠6= degrees m∠7= degrees m∠5= degrees

Explanation:

Step1: Vertical - angle property

$\angle2$ and $\angle4$ are vertical angles. Vertical angles are equal. So $m\angle4 = m\angle2=86^{\circ}$

Step2: Corresponding - angle property

$\angle2$ and $\angle6$ are corresponding angles. For parallel lines $m$ and $n$ cut by transversal $p$, corresponding angles are equal. So $m\angle6 = m\angle2 = 86^{\circ}$

Step3: Vertical - angle property

$\angle6$ and $\angle7$ are vertical angles. Vertical angles are equal. So $m\angle7=m\angle6 = 86^{\circ}$

Step4: Supplementary - angle property

$\angle5$ and $\angle6$ are supplementary angles (linear - pair). Since $m\angle6 = 86^{\circ}$, and $m\angle5+m\angle6 = 180^{\circ}$, then $m\angle5=180 - 86=94^{\circ}$

Answer:

$m\angle4 = 86$ degrees
$m\angle6 = 86$ degrees
$m\angle7 = 86$ degrees
$m\angle5 = 94$ degrees