Question

two rays and a line are shown. the measure of angle 2 is 40° more than the measure of angle 1. the measure of angle 3 is 10° more than the measure of angle 2. what is the measure of angle 3? a) 30° b) 50° c) 70° d) 80°

Explanation:

Step1: Express angles in terms of angle1

Let the measure of angle1 be \(x\). Then angle2 is \(x + 40\), and angle3 is \((x + 40)+10=x + 50\).

Step2: Use the straight - angle property

Since angle1, angle2, and angle3 form a straight - angle (\(180^{\circ}\)), we have \(x+(x + 40)+(x + 50)=180\).
Simplify the left - hand side: \(3x+90 = 180\).
Subtract 90 from both sides: \(3x=180 - 90=90\).
Divide both sides by 3: \(x = 30\).

Step3: Find the measure of angle3

Substitute \(x = 30\) into the expression for angle3 (\(x + 50\)). So angle3 is \(30+50 = 80^{\circ}\).

Answer:

d. \(80^{\circ}\)