Question

in the figure below, $m\angle 1=(x + 48)\degree$ and $m\angle 2 = 2x\degree$. find the angle measures. $m\angle 1 = \square\degree$ $m\angle 2 = \square\degree$

Explanation:

Step1: Recognize right angle sum

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

Step2: Substitute angle expressions

$(x+48) + 2x = 90$

Step3: Simplify and solve for x

$3x + 48 = 90$
$3x = 90 - 48$
$3x = 42$
$x = \frac{42}{3} = 14$

Step4: Calculate $m\angle 1$

$m\angle 1 = (14 + 48)^\circ = 62^\circ$

Step5: Calculate $m\angle 2$

$m\angle 2 = 2\times14^\circ = 28^\circ$

Answer:

$m\angle 1 = 62^\circ$
$m\angle 2 = 28^\circ$