Question

∠1 and ∠2 are supplementary. if m∠1 = (10x - 6)° and m∠2 = (3x - 9)°, find the measure of the larger angle
a 15°
b 36°
c 90°
d 114°

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \((10x - 6)+(3x - 9)=180\).

Step2: Simplify the equation

Combine like - terms: \(10x+3x-6 - 9 = 180\), which gives \(13x-15 = 180\).

Step3: Solve for \(x\)

Add \(15\) to both sides: \(13x=180 + 15=195\). Then divide by \(13\): \(x=\frac{195}{13}=15\).

Step4: Find the measures of \(\angle1\) and \(\angle2\)

For \(\angle1\): \(m\angle1=(10x - 6)^{\circ}\). Substitute \(x = 15\), \(m\angle1=(10\times15-6)^{\circ}=(150 - 6)^{\circ}=144^{\circ}\).
For \(\angle2\): \(m\angle2=(3x - 9)^{\circ}\). Substitute \(x = 15\), \(m\angle2=(3\times15-9)^{\circ}=(45 - 9)^{\circ}=36^{\circ}\).

Answer:

D. \(144^{\circ}\)