Question

∠a and ∠b are supplementary. ( m angle a = 2 x ) and ( m angle b = x - 15 ) what is the measure of the smaller angle? ( 20 ^ { circ } ) ( 50 ^ { circ } ) ( 35 ^ { circ } ) ( 65 ^ { circ } )

Explanation:

Step1: Use the supplementary angles property

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle A + m\angle B=180^{\circ}\). Substitute \(m\angle A = 2x\) and \(m\angle B=x - 15\) into the equation: \(2x+(x - 15)=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side: \(2x+x-15 = 180\), which gives \(3x-15 = 180\). Add \(15\) to both sides: \(3x=180 + 15=195\). Then divide both sides by \(3\): \(x=\frac{195}{3}=65\).

Step3: Find the measures of \(\angle A\) and \(\angle B\)

For \(\angle A\), \(m\angle A=2x\). Substitute \(x = 65\): \(m\angle A=2\times65 = 130^{\circ}\).
For \(\angle B\), \(m\angle B=x - 15\). Substitute \(x = 65\): \(m\angle B=65-15 = 50^{\circ}\).

Answer:

\(50^{\circ}\)