In the figure below, angle y and angle x form vertical angles. angle x forms a straight line with the 50° angle and the 40° angle.

write and solve an equation to determine the measure of angle y.

Measure of ∠y is 90°

Step-by-step explanation:

We see that,

∠x and ∠y are vertical angles and ∠x, 40°, 50° are in a straight line.

Since, we know, Sum of angles in straight line is 180°.

Then, ∠x + 40° + 50° = 180°

i.e. ∠x = 180° - 90°

i.e. ∠x = 90°

Also, we know, 'Vertical angles have equal measures'.

So, ∠y = ∠x = 90°

Hence, measure of ∠y is 90°

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.

the correct answer would be:

220 centimeters

to get this you can use the pythagorean theorem

hope this

step-by-step explanation: