Question

Need help finding measure of angle R.

Answer 1

Answer:

B.) 113°

Step-by-step 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:

$\frac{45}{3}=\frac{3x}{3}\\\\ 15=x\\\\x=15$

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:

$\frac{226}{2}= 113$

Angle R is 113°.

Done.