Question

in the figure below, $m\angle 1 = 3x^\circ$ and $m\angle 2 = (x + 68)^\circ$. find the angle measures. $m\angle 1 = \square^\circ$ $m\angle 2 = \square^\circ$

Explanation:

Step1: Recognize supplementary angles

The angles form a straight line, so $m\angle 1 + m\angle 2 = 180^\circ$.

Step2: Substitute angle expressions

$3x + (x + 68) = 180$

Step3: Simplify and solve for $x$

$4x + 68 = 180$
$4x = 180 - 68$
$4x = 112$
$x = \frac{112}{4} = 28$

Step4: Calculate $m\angle 1$

$m\angle 1 = 3x = 3\times28 = 84$

Step5: Calculate $m\angle 2$

$m\angle 2 = x + 68 = 28 + 68 = 96$

Answer:

$m\angle 1 = 84^\circ$
$m\angle 2 = 96^\circ$