Use rectangle ABCD and the given information to solve each problem.

Given: m<9= 80°

Find:
m<6_
m<7_
m<8_

2. Given: m<5= 29°

Find:
m<2_
m<3_

Problem 1

Work Shown:

point E = intersection point of diagonals.

x = measure of angle 6

y = measure of angle 8

angle 7 is also x because triangle AED is isosceles (AE = ED)

Focus on triangle AED, the three angles A, E, D add to 180

A+E+D = 180

x+80+x = 180

2x+80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

So both angles 6 and 7 are 50 degrees.

Turn to angle 8. This is adjacent to angle 7. The two angles form a 90 degree angle at point A. This is because a rectangle has 4 right angles.

(angle7)+(angle8) = 90

50+y = 90

y = 90-50

y = 40

angle 8 = 40 degrees

Problem 2

Work Shown:

Angle 5 is 29 degrees (given). So is angle 4 because these are the base angles of isosceles triangle DEC (segment DE = segment EC)

angle 3 and angle 4 form a 90 degree angle

x = measure of angle 3

(angle 3)+(angle 4) = 90

x+29 = 90

x = 90-29

x = 61

Angle 2 is congruent to angle 3 since triangle BEC is isosceles (BE = EC), so both angle 2 and angle 3 are 61 degrees each.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i