Question

find the measures of the labeled angles. HELP ASAP PLEASE

Answer 1

(x + 87)° = 116°

We can see that the angle of (x + 87)° is directly across from the angle of 4x°. This shows that they are equal. We can take the two terms and make an equation.

—> (x + 87) = 4x

After solving for the value of x, we get a value of 29.

Now that we know x, let's substitute it into (x + 87).

(x + 87) becomes (29 + 87), which is equal to 116°.

To check, we can substitute 29 into the other angle of 4x as well, since the two angles are equal.

4x becomes 4(29), which is also equal to 116°.

Answer 2

The measures of the labelled angles that are vertically opposite to each other are:

x + 87 = 116 degrees

4x = 116 degrees

(x + 87) and 4x are vertical angles directly opposite each other.

According to the vertical angles theorem, (x + 87) and 4x are congruent.

• Therefore, we will have:

(x + 87) = 4x

• Solve to find the value of x

x + 87 = 4x

• Subtract x from both sides

x + 87 - x = 4x - x

87 = 3x

• Divide both sides by 3

29 = x

x = 29

Find the labelled angles by plugging in the value of x

• x + 87 = 29 + 87 = 116 degrees

• 4x = 4(29) = 116 degrees

Therefore, the measures of the labelled angles that are vertically opposite to each other are:

x + 87 = 116 degrees

4x = 116 degrees

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