Question

Need help finding measure of angle R.

Answer 1

B.) 113°

Explanation:

In the isosceles trapezoid, angles T and S are congruent. Find the value of x:

`4x+7=7x-38`

Subtract 4x from both sides:

`4x-4x+7=7x-38-4x\\7=3x-38`

Add 38 to both sides:

`7+38=3x-38+38\\45=3x`

Divide both sides by 3:

`(45)/(3)=(3x)/(3)\\\\ 15=x\\\\x=15`

x is equal to 15. Now substitute the value of x into the one of the expressions:

`4(15)+7\\60+7\\67`

or

`7(15)-38\\105-38\\67`

The angles T and S are 67°.

The angles of a trapezoid will always add up to a total of 360°, so add the angles T and S:

`67+67=134`

Subtract their total from 360:

`360-134=226`

The total of the angles Q and R is 226°. Since this is an isosceles trapezoid, those two angles are also congruent. Divide the value by 2:

`(226)/(2)= 113`

Angle R is 113°.

Done.