What is the value of x in the figure? enter your answer in the box. x = three lines creating six angles with the top left angle having a square on it indicating a right angle, the top right angle labeled as sixty one degrees and the angle between them labeled as x degrees

Three lines creating six angles

3 angles on top, 3 angles below

Since the top left angle is a right angle

It means the line that divides the top angles from the angles below is bisected by a perpendicular line.

This means the sum of the angles of the top left = 90°

Therefore, x + 61° = 90°

x = 90° – 61°

x = 29°

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.