To find the measure of ∠PQT, we need to use the fact that QS bisects ∠PQT.
By the angle bisector theorem, we know that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the measures of the angles formed by the angle bisector.
In this case, we have QS bisecting ∠PQT, so we can set up the following proportion:
QS/ST = ∠PQS/∠SQT
Given that ∠SQT = (8x−25)° and ∠PQT = (9x+34)°, we can substitute these values into the proportion:
QS/ST = (9x+34)/(8x−25)
To solve for x, we can cross-multiply:
QS * (8x−25) = ST * (9x+34)
Expanding both sides of the equation:
8xQS − 25QS = 9xST + 34ST
Rearranging terms:
8xQS - 9xST = 25QS + 34ST
Factoring out x:
x(8QS - 9ST) = 25QS + 34ST
Dividing both sides by (8QS - 9ST):
x = (25QS + 34ST)/(8QS - 9ST)
Now, we don't have enough information to find the exact measure of ∠PQT, but if you were given actual values for QS and ST, you could substitute them into the equation above to solve for x and find the measure of ∠PQT.
If QS−→
bisects ∠PQT
. If ∡SQT =
(8x−25)°
and ∡PQT =
(9x+34)°
find the measure of ∠PQT
(2 points)
∡PQT
=
°
1 answer