To find the measures of the two unknown angles, we start by setting up the equation based on the information given.
The two adjacent angles are \(x - 5\) and \(3x\). The sum of their measures is given as 107 degrees:
\[ (x - 5) + (3x) = 107 \]
Now, combine like terms:
\[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \]
Next, add 5 to both sides of the equation:
\[ 4x = 107 + 5 \] \[ 4x = 112 \]
Now, divide both sides by 4 to solve for \(x\):
\[ x = \frac{112}{4} = 28 \]
Now that we have the value of \(x\), we can find the measures of the two angles:
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The first angle: \[ x - 5 = 28 - 5 = 23 \]
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The second angle: \[ 3x = 3 \times 28 = 84 \]
Thus, the two angle measures are \(23\) and \(84\).
Now, let's check the options provided:
- 28 and 79
- 20 and 87
- 23 and 84
- 32 and 75
The correct answer is \(\boxed{23}\) and \(\boxed{84}\).
1 answer