Question

in the figure below, $m\angle 1 = 5x^\circ$ and $m\angle 2 = (x - 12)^\circ$. find the angle measures. $m\angle 1 = \square^\circ$ $m\angle 2 = \square^\circ$

Explanation:

Step1: Recognize right angle sum

The two angles form a right angle, so their sum is $90^\circ$.
$m\angle1 + m\angle2 = 90^\circ$

Step2: Substitute angle expressions

Replace the angles with given algebraic expressions.
$5x + (x - 12) = 90$

Step3: Simplify and solve for $x$

Combine like terms and isolate $x$.
$6x - 12 = 90$
$6x = 102$
$x = 17$

Step4: Calculate $m\angle1$

Substitute $x=17$ into $5x$.
$m\angle1 = 5\times17 = 85$

Step5: Calculate $m\angle2$

Substitute $x=17$ into $x-12$.
$m\angle2 = 17 - 12 = 5$

Answer:

$m\angle1 = 85^\circ$
$m\angle2 = 5^\circ$