Question

in the figure below, m∠1=(x - 6)° and m∠2 = 5x°. find the angle measures.

Explanation:

Step1: Note angle - sum property

$\angle1+\angle2 = 180^{\circ}$ (linear - pair of angles).

Step2: Substitute angle expressions

$(x - 6)+5x=180$.

Step3: Combine like - terms

$6x-6 = 180$.

Step4: Solve for x

$6x=186$, so $x = 31$.

Step5: Find $\angle1$ and $\angle2$

$m\angle1=(x - 6)^{\circ}=(31 - 6)^{\circ}=25^{\circ}$; $m\angle2 = 5x^{\circ}=5\times31^{\circ}=155^{\circ}$.

Answer:

$m\angle1 = 25^{\circ}$, $m\angle2 = 155^{\circ}$