Question

What is the measure of angle 7?

The measure of angle 1 is (3x + 10)° and the measure of
angle 4 is (4x - 15)
6 8
24
5 7
1
3

Answer 1

Explanation:

So m<1 = m<4 because of vertical angle theorem. That means that you can say:

(3x+10) = (4x -15) now solve

3x + 10 = 4x - 15

10 = x - 15

25 = x

now put it back into the equation

m<1 = (3x + 10) = 3*25 + 10 = 85

m<4 = (4x - 15) = 4*25 - 15 = 85

either way it's both 85º.

<3 is the supplementary angle of <1 (adjacent angles)

now < 3 + < 1 = 180º

so < 3 + 85º = 180º

< 3 = 95º

m<7 is also equal to m<3. This is because of corresponding angles.

so m<7 is also = 95º

correct me if i'm wrong and ask more questions!

Answer 2

95°

Explanation:

1) the angles one and four are equivalent so you can equate the expressions given for their values and get:

3x+10=4x-15

if you combine like terms you will get that x = 25

2) plug in your x value into one of the expressions to get the value for that angle and you should get 85.

3) because angles 1 and 7 are corresponding exterior angles we know that they add up to 180°. so we can make the following equation:

x+85°=180°

4) solve for x and you have your answer