In quadrilateral QRST, m∠Q is 68°, m∠R is (3x + 40)°, and m∠T is (5x − 52)°. What are the measures of ∠R , ∠S , and ∠T ? Write the numerical values in that order with the measures separated by commas.

Question

In quadrilateral QRST, m∠Q  is 68°, m∠R  is (3x + 40)°, and m∠T  is (5x − 52)°. What are the measures of ∠R , ∠S , and ∠T ? Write the numerical values in that order with the measures separated by commas.

mathstudent55 · Answer

There isn't enough info. Is there a figure?

anonymous · Answer

it wont let me post it :(

anonymous · Answer

nvm

mathstudent55 · Answer

Ok. That's the extra info.
The quadrilateral is inscribed in a circle.

mathstudent55 · Answer

In an inscribed quadrilateral, opposite angles are supplementary.

anonymous · Answer

The opposite angles of a quadrilateral inscribed in a circle are supplementary:
m∠Q+m∠S= 180°  
m∠S=180°−m∠Q=180°−68°= 112°  
   m∠R+m∠T=180°  
(3x + 40) + (5x − 52) = 180° 
Solving for x, x = 24°.
Substituting the value of x in the expressions for m∠R  and 
m∠T   , m∠R  = 112° and m∠T  = 68°.

campbell_st · Answer

well the opposite angles in a cyclic quadrilateral are supplementary

mathstudent55 · Answer

Angles Q and S are opposite angles.
They are supplementary.
Can you find the measure of angle S?

anonymous · Answer

it tells me to put it with commas??? i don't understand ..

mathstudent55 · Answer

1, 2, 3, 4
Numbers separated by commas.

mathstudent55 · Answer

Only 3 numbers, though.

anonymous · Answer

ok ooohhh i get it ok :) thank you! ^.^

mathstudent55 · Answer

yw

anonymous · Answer

so how would it actually be with the commas?

anonymous · Answer

can someone help me?

anonymous · Answer

m∠Q+m∠S= 180° 
m∠S=180°−m∠Q=180°−68°= 112° 
m∠R+m∠T=180° 
(3x + 40) + (5x − 52) = 180° 
Solving for x, x = 24°.
Substituting the value of x in the expressions for m∠R and 
m∠T , m∠R = 112° and m∠T = 68°

anonymous · Answer

how do i write the answer

anonymous · Answer

112,112,68 can i get a medal :)