To find the value of \( x \) and the measures of the angles, we first need to write the equation based on the relationships given in the problem.
(a) Write an equation to find \( x \).
From the information provided, we have: \[ m∠1 = x + 14° \] \[ m∠2 = 3x° \]
Usually, if these two angles are related (for instance, if they are vertical angles, supplementary, or complementary), we would add or set them equal to each other. However, since the information regarding their relationship is not specified, we will assume they are equal for this purpose.
Thus, we can set the two angle expressions equal to each other: \[ x + 14° = 3x° \]
Equation:
\[ x + 14° = 3x° \]
(b) Find the degree measure of each angle.
To solve for \( x \), we rearrange the equation: \[ 14° = 3x° - x \] \[ 14° = 2x° \] \[ x = \frac{14}{2} = 7° \]
Now we can find the measures of each angle:
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For \( m∠1 \): \[ m∠1 = x + 14° = 7° + 14° = 21° \]
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For \( m∠2 \): \[ m∠2 = 3x° = 3(7°) = 21° \]
Hence, the degree measures of the angles are:
- \( m∠1 = 21° \)
- \( m∠2 = 21° \)
Final Answers:
- \( m∠1 = 21° \)
- \( x = 7° \)