Question

in the figure below, m∠1 = 5x° and m∠2=(x - 18)°. find the angle measures.

Explanation:

Step1: Note angle - sum property

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

Step2: Substitute angle expressions

$5x+(x - 18)=90$

Step3: Simplify the equation

$6x-18 = 90$
$6x=90 + 18$
$6x=108$
$x = 18$

Step4: Find $\angle1$ and $\angle2$

$m\angle1=5x=5\times18 = 90^{\circ}$
$m\angle2=x - 18=18-18 = 0^{\circ}$

Answer:

$m\angle1 = 90^{\circ}$, $m\angle2 = 0^{\circ}$