Question

the angles are supplementary angles. determine the measures of ∠1 and ∠2. m∠1 = □°, and m∠2 = □°

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(x+(3x - 4)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+3x-4 = 180\) becomes \(4x-4 = 180\).

Step3: Solve for \(x\)

Add 4 to both sides of the equation: \(4x-4 + 4=180 + 4\), which gives \(4x=184\). Then divide both sides by 4: \(x=\frac{184}{4}=46\).

Step4: Find the measure of \(\angle1\)

Substitute \(x = 46\) into the expression for \(\angle1\) (which is \(3x-4\)). So, \(m\angle1=3\times46-4=138 - 4=134^{\circ}\).

Step5: Find the measure of \(\angle2\)

Since \(x\) represents the measure of \(\angle2\), \(m\angle2 = 46^{\circ}\).

Answer:

\(m\angle1 = 134^{\circ}\), and \(m\angle2 = 46^{\circ}\)