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If angle 2 = 6x + 5 and angle 4 = 4x + 14, what is the value of angle 2? Round your answer to the hundredths place.

If angle 2 = 6x + 5 and angle 4 = 4x + 14, what is the value of angle 2? Round your-example-1
User Sudhir Bhapkar
by
2.9k points

1 Answer

8 votes
8 votes

Answer:

32°

Explanation:

Angles 2 and 4 are vertical angles, so they are congruent. That means that their measures are equal.

First, we set their measures equal to each other.

Then we solve the equation for x.

Then, we use the value of x to find the angle measure.

m<2 = 6x + 5

m<4 = 4x + 14

Set the measures equal.

6x + 5 = 4x + 14

Subtract 4x from both sides.

2x + 5 = 14

Subtract 5 from both sides.

2x = 9

Divide both sides by 2.

x = 4.5

m<2 = 6x + 5

m<2 = 6 × 4.5 + 5

m<2 = 27 + 5

m<2 = 32

Answer: 32°

User Bojan
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3.2k points