Answer:
B.) 113°
Step-by-step explanation:
In the isosceles trapezoid, angles T and S are congruent. Find the value of x:
[tex]4x+7=7x-38[/tex]
Subtract 4x from both sides:
[tex]4x-4x+7=7x-38-4x\\7=3x-38[/tex]
Add 38 to both sides:
[tex]7+38=3x-38+38\\45=3x[/tex]
Divide both sides by 3:
[tex]\frac{45}{3}=\frac{3x}{3}\\\\ 15=x\\\\x=15[/tex]
x is equal to 15. Now substitute the value of x into the one of the expressions:
[tex]4(15)+7\\60+7\\67[/tex]
or
[tex]7(15)-38\\105-38\\67[/tex]
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:
[tex]67+67=134[/tex]
Subtract their total from 360:
[tex]360-134=226[/tex]
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:
[tex]\frac{226}{2}= 113[/tex]
Angle R is 113°.
Done.
