Question

QUESTIONS BELOW! PLEASE HELP DONT KNOW WHERE TO START IM CONFUSED AND NEED THIS DONE!

Answer 1

The measures of the angles are

• Figure 1: <1 = 110 --- angle on a straight line
• Figure 1: <2 = 25 --- base angle of an isosceles triangle
• Figure <2: <1  = 55 -- angles in a triangle
• Figure <2: <2  = 65 -- angles in a triangle
• Figure <2: <3 = 30 -- -corresponding angles
• Figure <2: <4 = 120 --- external angle of a triangle
• Figure 3: <1 = 30 --- angles in a triangle
• Figure 3: <2 = 25 --- corresponding angles

How to determine the measures of the angles

Figure 1

The angle on a straight line is 180 degrees

So, we have

<1 + 70 = 180

Evaluate

<1 = 110 --- angle on a straight line

Also, we have

<2 + <2 + <1 = 180

This gives

2 * <2 + 110 = 180

So, we have

2 * <2 = 180 - 110

Evaluate

<2 = 25 --- base angle of an isosceles triangle

Figure 2

The angles in a triangle is 180 degrees

So, we have

<2 + 25 + 90 = 180

Evaluate

<2 = 65

The angles in a triangle line is 180 degrees

So, we have

<1 + <2 + 60 = 180

<1 + 65 + 60 = 180

This gives

<1  = 55

Corresponding angles are equal.

So, we have

<3 + 25 = <1

<3 + 25 = 55

Evaluate

<3 = 30

By the theorem of external angle of a triangle, we have

<4 = 90 + <3

<4 = 90 + 30

<4 = 120

Figure 3

By corresponding angles, we have

<2 = 75

The angle on a straight line is 180

So, we have

x = 180 - 75 - <2

x = 180 - 75 - 75

x = 30

By the sum of angles in a triangle, we have

<1 = 180 - 120 - x

<1 = 180 - 120 - 30

<1 = 30

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