Question

a. Find the value of x given that r ll s.The measure of angle 1 = (63-x)The measure of angle 2 = (72-2x)b. Find the measure of angle 1 and the measure of angle 2.

Answer 1

In the given illustration, angle 1 and angle 2 are corresponding angles.

Note that corresponding angles in parallel lines are congruent.

angle 1 measures (63 - x)

angle 2 measures (72 - 2x)

Since both angles are congruent with each other, equate the angles :

`\begin{gathered} 63-x=72-2x \\ \text{Solve for x, put the variables to the left side and the constant to the right side :} \\ -x+2x=72-63 \\ x=9 \end{gathered}`

The measure of angle 1 will be :

`63-9=54`

The measure of angle 2 will be :

`72-2(9)=54`

ANSWERS :

a. x = 9

b. angle 1 = 54 degrees

angle 2 = 54 degrees