Question

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

Explanation:

Step1: Note angle - sum relationship

$\angle1+\angle2 = 90^{\circ}$ (complementary angles)

Step2: Substitute angle expressions

$6x+(x + 6)=90$

Step3: Combine like - terms

$7x+6 = 90$

Step4: Solve for x

$7x=90 - 6=84$, so $x = 12$

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

$m\angle1=6x=6\times12 = 72^{\circ}$, $m\angle2=x + 6=12+6 = 18^{\circ}$

Answer:

$m\angle1 = 72^{\circ}$, $m\angle2 = 18^{\circ}$