To solve the problem, we need to establish an equation based on the information given about the angles.
Let's write the equation from the information provided:
(a) The angles are given as:
- \( m \angle 1 = 15x^\circ \)
- \( m \angle 2 = x + 12^\circ \)
Assuming that these two angles are equal (given them in the same context), we can write the equation:
\[ 15x = x + 12 \]
(b) Now, we will solve for \( x \):
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Start by subtracting \( x \) from both sides: \[ 15x - x = 12 \] This simplifies to: \[ 14x = 12 \]
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Next, divide both sides by 14: \[ x = \frac{12}{14} = \frac{6}{7} \]
Now we will calculate the degree measure of each angle using the value of \( x \).
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First, find \( m \angle 1 \): \[ m \angle 1 = 15x = 15 \times \frac{6}{7} = \frac{90}{7} \approx 12.857^\circ \]
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Next, find \( m \angle 2 \): \[ m \angle 2 = x + 12 = \frac{6}{7} + 12 = \frac{6}{7} + \frac{84}{7} = \frac{90}{7} \approx 12.857^\circ \]
Thus, both angles are actually equal.
The angles in degrees are approximately:
- \( m \angle 1 \approx 12.857^\circ \)
- \( m \angle 2 \approx 12.857^\circ \)
To summarize:
(a) The equation is: \[ 15x = x + 12 \]
(b) The degree measure of each angle is:
- \( m \angle 1 \approx 12.857^\circ \)
- \( m \angle 2 \approx 12.857^\circ \)