Question

Complementary, Supplementary, Vertical, and Adjacent Angles
100 POINTS

Answer 1

1) d. All of the above are true

2) b. 21.8°

3) 7x + 10 = 150 ; x = 20°

4) b. The measure of angle B is 117°

Explanation:

1) 4x + 8x = 180

12x = 180

x = 15°

4x = 60°

8x = 120°

2) x = 90 - 68.2

x = 21.8°

3) 7x + 10 = 150

(Vertically opposite angles)

7x = 140

x = 20°

4) Angle A = 180 - 90 - 27

Angle A = 63°

Angle B = 180 - 63

Angle B = 117°

Angle C = 180 - 117

Angle C = 63°

Answer 2

Explanation:

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QUESTION 1: B

Half of a circle is 180. One side is 27° and the one in the middle is a right angle which is 90°. So we must add the sides together than subtract them by 180°.

90° + 27° = 117°

180° - 117° = 63°

So now we know that angle A is 63°!

Angle C is adjacent to angle A making it 63° as well. We also know that angle B is adjacent so that means angle B is 117°.

Only B is is the correct answer.

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QUESTION 2: x = 20

150° is adjacent to 7x + 10 making them equal. But how do we solve this? We must make a linear equation out of this!

150 = 7x + 10

Subtract 10 on each side,

150 = 7x + 10

- 10 - 10

We get,

140 = 7x

Divide by 7 on each side,

140 ÷ 7 = 7x ÷ 7

Evaluate,

20 = x

We get that our answer is x = 20!

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QUESTION 3: x = 21.8°

We know that x° + 68.2° = 90° or a right angle. Therefore for this problem we must subtract!

90° - 68.2° = 21.8°

For this question x is 21.8°

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QUESTION 4:

For this question we know that 4x + 8x = 180° we must solve this linear equation out!

4x + 8x = 180°

Add,

12x = 180°

Divide by 12,

12x ÷ 12 = 180° ÷ 12

Evaluate,

x = 15

We now know that x = 15 which solves our 4th and final question of the day! Phew! That took a lot of brain power but we made it! Nice job everyone!