Question

8 find the measure of each angle. ∠1 and ∠2 are vertical angles, m∠1 = (17x + 3)°, and m∠2 = (20x - 15)°. find m∠1 and m∠2. m∠1 = □° m∠2 = □°

Explanation:

Step1: Set angles equal (vertical angles)

$17x + 3 = 20x - 15$

Step2: Solve for x

$3 + 15 = 20x - 17x$
$18 = 3x$
$x = \frac{18}{3} = 6$

Step3: Calculate m∠1

$m\angle1 = 17(6) + 3 = 102 + 3 = 105$

Step4: Verify m∠2 (optional)

$m\angle2 = 20(6) - 15 = 120 - 15 = 105$

Answer:

$m\angle1 = 105^\circ$
$m\angle2 = 105^\circ$