Answer :
The measure angle of QPS is 99 degrees
What is arc?
The arc of a circle is defined as the part or segment of the circumference of a circle.
we find that angles QPS is equal to 34 degrees using the angle sum property of a triangle
we have a line segment PS and a transversal QR intersecting at point T. we are given that the measure of angle PQT IS 4x-1 and the measure of angle RQT IS 12x-27 we need to find the measure of angle QPS.
How we can calculate?
since angle PQT and angle RQT are opposite angles, they are congruent, so we can write
mPQT = mRQT
4x-1 = 12x-27
x=13/4
now we can substitute x=13/4 in the expressions for mPQT and mQPS to find their measures:
mPQT = 4x-1 =4(13/4) -1 = 12
mQPS = 180 - mPQT-mRQT=180-12-(12(13/4)-27)=99
therefore the measure angle QPS is 99 degrees.
To learn more about angle visit:
https://brainly.com/question/25716982
#SPJ1
Step-by-step explanation:
