Question

find the measure of the marked angles.
(3x + 30)°
(8x + 5)°
the measure of the angles is □ degrees.

Explanation:

Step1: Identify vertical angles

Vertical angles are equal, so set \(3x + 30 = 8x + 5\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(30 = 5x + 5\).
Subtract 5: \(25 = 5x\).
Divide by 5: \(x = 5\).

Step3: Find angle measure

Substitute \(x = 5\) into \(3x + 30\): \(3(5) + 30 = 15 + 30 = 45\).
(Or into \(8x + 5\): \(8(5) + 5 = 40 + 5 = 45\).)

Answer:

45