the measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x - 15)°. what is the measure of angle 7?

Explanation:

Step1: Identify angle - relationship

Assume lines (a), (b) are parallel and (c) is a transversal. Angle 1 and angle 4 are corresponding angles, so they are equal. (3x + 10=4x - 15)

Step2: Solve for (x)

Subtract (3x) from both sides: (10=x - 15). Then add 15 to both sides. (x=10 + 15=25)

Step3: Find the measure of angle 1

Substitute (x = 25) into the expression for angle 1: (3x+10=3\times25 + 10=75 + 10=85^{\circ})

Step4: Identify the relationship between angle 1 and angle 7

Angle 1 and angle 7 are vertical - angles. Vertical angles are equal. So the measure of angle 7 is also (85^{\circ})

Answer:

(85)