Question

find the measure of each numbered angle: 18° 94° 61°

Explanation:

Step1: Find angle 2

Vertical angles are equal, so angle 2 is equal to the 94° angle. So, $m\angle 2 = 94^\circ$.

Step2: Find angle 1

In a triangle, the sum of angles is $180^\circ$. For the triangle with angle 1, 18°, and 94° (vertical angle of angle 2), we have:
$m\angle 1 + 18^\circ + 94^\circ = 180^\circ$
$m\angle 1 = 180^\circ - 18^\circ - 94^\circ$
$m\angle 1 = 68^\circ$

Step3: Find angle 3

In the triangle with angle 3, 61°, and angle 2 (94°), we use the triangle angle sum:
$m\angle 3 + 61^\circ + 94^\circ = 180^\circ$
$m\angle 3 = 180^\circ - 61^\circ - 94^\circ$
$m\angle 3 = 25^\circ$

Answer:

$m\angle 1 = 68^\circ$, $m\angle 2 = 94^\circ$, $m\angle 3 = 25^\circ$