To find the measures of angles A and C, we can first set up the equations based on the information provided:
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For angle A: \[ m∠A = 2x \]
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For angle B: \[ m∠B = 96^\circ \]
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For angle C: \[ m∠C = x + 12 \]
Since the sum of the angles in a triangle is always \(180^\circ\), we have: \[ m∠A + m∠B + m∠C = 180 \] Substituting the expressions we have: \[ 2x + 96 + (x + 12) = 180 \] Now, simplify the equation: \[ 2x + 96 + x + 12 = 180 \] Combining like terms: \[ 3x + 108 = 180 \] Next, isolate \(x\) by subtracting \(108\) from both sides: \[ 3x = 180 - 108 \] \[ 3x = 72 \] Now, divide by \(3\): \[ x = 24 \]
Now that we have \(x\), we can find the measures of angles A and C.
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Calculate \(m∠A\): \[ m∠A = 2x = 2(24) = 48^\circ \]
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Calculate \(m∠C\): \[ m∠C = x + 12 = 24 + 12 = 36^\circ \]
So, the measures of the missing angles are:
- \(m∠A = 48^\circ\)
- \(m∠C = 36^\circ\)
Thus, the final answers are:
- m∠A = 48°
- m∠C = 36°