Question

in the figure below, ( mangle 1 = 5x^circ ) and ( mangle 2 = (x + 12)^circ ). find the angle measures.
( mangle 1 = square^circ )
( mangle 2 = square^circ )

Explanation:

Step1: Set sum to 90°

$\angle 1 + \angle 2 = 90^\circ$

Step2: Substitute angle expressions

$5x + (x + 12) = 90$

Step3: Simplify and solve for x

$6x + 12 = 90$
$6x = 78$
$x = 13$

Step4: Calculate $m\angle 1$

$m\angle 1 = 5 \times 13 = 65$

Step5: Calculate $m\angle 2$

$m\angle 2 = 13 + 12 = 25$

Answer:

$m\angle 1 = 65^\circ$
$m\angle 2 = 25^\circ$