Question

what is the value of x? find the measure of angle 3. (diagram: two lines intersected by a vertical transversal; one angle labeled ( 61^circ ), another labeled ( 4x + 1 ); points labeled 2, 3, 5, 6, 7, 8. input interface (keyboard) and skill code: 1062113.)

Explanation:

Step1: Identify parallel lines and transversal

The two slanted lines are parallel, and the vertical line is a transversal. So, the corresponding angles are equal. Thus, \(4x + 1=61\).

Step2: Solve for \(x\)

Subtract 1 from both sides: \(4x=61 - 1=60\).
Divide both sides by 4: \(x=\frac{60}{4} = 15\).

Angle 3 and the angle with measure \(61^{\circ}\) are supplementary (they form a linear pair). So, \(m\angle3 = 180^{\circ}-61^{\circ}=119^{\circ}\).

Answer:

15

For the measure of angle 3: