If QS−→bisects ∠PQT. If ∡SQT = (8x−25)° and ∡PQT = (9x+34)°find the measure of ∠PQT
Since QS bisects ∠PQT, we can set ∡SQT equal to ∡PQT.
So, (8x−25) = (9x+34)
Simplifying the equation, we get:
8x − 25 = 9x + 34
Subtracting 8x from both sides, we get:
-25 = x + 34
Subtracting 34 from both sides, we get:
-59 = x
Thus, the measure of ∠PQT is:
∡PQT = 9x + 34
= 9(-59) + 34
= -531 + 34
= -497
Therefore, the measure of ∠PQT is -497 degrees.
To find the measure of angle PQT, we need to equate the measures of angles SQT and PQT, as QS-→ bisects angle PQT.
Given:
Angle SQT = (8x - 25)°
Angle PQT = (9x + 34)°
Since QS-→ bisects angle PQT, we have:
Angle SQT = Angle PQT
Setting these two expressions equal:
(8x - 25)° = (9x + 34)°
Now, we can solve for x:
8x - 25 = 9x + 34
Subtracting 8x from both sides:
-25 = x + 34
Subtracting 34 from both sides:
-59 = x
Now, we substitute the value of x back into the expression for angle PQT to find its measure:
Angle PQT = (9x + 34)°
= (9(-59) + 34)°
= (-531 + 34)°
= -497°
Therefore, the measure of angle PQT is -497°.