What is m∠aeb?

enter your answer in the box.

°

line b d is slightly inclined with vertical intersects with line a c at e. point c is on right side of line b d. the left upward and right downward angles of the intersecting lines are obtuse. the measure of angle a e b is labeled as left parenthesis 5 x minus 10 right parenthesis degrees. the measure of angle c e d is labeled as left parenthesis 3 x plus 40 right parenthesis degrees.

m∠AEB=115°

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. Vertical angles are always congruent.

In this problem

m∠AEB=m∠CED -----> by vertical angles

substitute the values

Solve for x

Find out the measure of m∠AEB

m∠AEB=(5x-10)°

substitute the value of x

m∠AEB=(5(25)-10)=115°

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.