Chapter 5.6, Problem 17PSB

To determine

To calculate:Thevalue of x.

Answer to Problem 17PSB

Thevalue of xis${145}^{\circ }$ .

Explanation of Solution

Given information:

Line a is parallel to line b.

A ${55}^{\circ }$ angle is made on line b.

Calculation:

  

Parallel postulate states that through any given point not on a line there passes exactly one line parallel to that line in the same plane.

By Parallel postulate, draw line mparallel to line a.

  $\angle 2={90}^{\circ }$

If lines are parallel then there interior angles are supplementary.

  $\angle 3={90}^{\circ }$ , its supplementary is ${90}^{\circ }$ .

Line a is parallel to line b.

By transitive property, we get

Line m is parallel to lineb.

If lines are parallel then there interior angles are congruent.

  $\angle 1={55}^{\circ }$

The value of x is:

  $x={90}^{\circ }+{55}^{\circ }={145}^{\circ }$