Need help finding measure of angle R.

Question

asked Nov 27, 2021 185k views

1 Answer

Andrey Izman · Answer 1 · 2021-12-02T02:06:50+0000

Answer:

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.