Question

If ray QS bisects angle PQR, angle PQS = 7x - 6 degrees, and angle SQR = 4x + 15 degrees, find angle PQT. O 7 O 21 O 43 O 94

Answer 1

To find angle PQT, we need to use the fact that ray QS bisects angle PQR. When a ray bisects an angle, it divides the angle into two equal parts. So, angle PQS is equal to angle SQR. Using this information, we can set up an equation: 7x - 6 = 4x + 15.

Step-by-step explanation:

To find angle PQT, we need to use the fact that ray QS bisects angle PQR. When a ray bisects an angle, it divides the angle into two equal parts. So, angle PQS is equal to angle SQR. Using this information, we can set up an equation:

7x - 6 = 4x + 15

Now, we can solve the equation to find the value of x.

7x - 4x = 15 + 6

3x = 21

x = 7

Now that we know the value of x, we can substitute it back into the equations to find the angles:

Angle PQS = 7(7) - 6 = 43 degrees

Angle SQR = 4(7) + 15 = 43 degrees

Since ray QS bisects angle PQR, angle PQT is equal to half of angle PQR. So, angle PQT is 43 degrees divided by 2, which equals 21.5 degrees. Since the answer choices are given in whole numbers, we round down and the final answer is 21 degrees.