Question

in the figure below, ( mangle1 = 3x^{circ} ) and ( mangle2=(x + 88)^{circ} ). find the angle measures.
( mangle1=)( mangle2=)

Explanation:

Step1: Set up the equation

Since ∠1 and ∠2 are supplementary (they form a linear pair), \(m\angle1 + m\angle2=180^{\circ}\). Substitute \(m\angle1 = 3x\) and \(m\angle2=(x + 88)\) into the equation: \(3x+(x + 88)=180\).

Step2: Simplify the equation

Combine like - terms: \(3x+x+88 = 180\), which gives \(4x+88 = 180\).

Step3: Solve for \(x\)

Subtract 88 from both sides: \(4x=180 - 88\), so \(4x=92\). Then divide both sides by 4: \(x=\frac{92}{4}=23\).

Step4: Find \(m\angle1\) and \(m\angle2\)

For \(m\angle1\): Substitute \(x = 23\) into \(m\angle1=3x\), so \(m\angle1=3\times23 = 69^{\circ}\).
For \(m\angle2\): Substitute \(x = 23\) into \(m\angle2=(x + 88)\), so \(m\angle2=23+88 = 111^{\circ}\).

Answer:

\(m\angle1 = 69^{\circ}\), \(m\angle2 = 111^{\circ}\)