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Two vertical angles are given as (6x−15)° and (4x+5)°. What is the measure of each angle?

(4 Points)

35°

45°

55°

65°

1 answer

To find the measure of each angle given that they are vertical angles, we can set them equal to each other because vertical angles are congruent.

We have:

\[ 6x - 15 = 4x + 5 \]

Now, let's solve for \(x\).

  1. Subtract \(4x\) from both sides: \[ 6x - 4x - 15 = 5 \] \[ 2x - 15 = 5 \]

  2. Add 15 to both sides: \[ 2x = 20 \]

  3. Divide by 2: \[ x = 10 \]

Now that we have the value of \(x\), we can find the measure of each angle.

  1. Calculate the first angle: \[ 6x - 15 = 6(10) - 15 = 60 - 15 = 45° \]

  2. Calculate the second angle: \[ 4x + 5 = 4(10) + 5 = 40 + 5 = 45° \]

Therefore, both vertical angles measure 45°.

So the answer is 45°.