Question

in the figure below, ( m angle 1=(x + 72)^{circ} ) and ( m angle 2=2 x^{circ} ). find the angle measures.
( m angle 1=square^{circ} )
( m angle 2=square^{circ} )

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle1\) and \(\angle2\) are supplementary (they form a linear - pair), \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(x + 72)^{\circ}\) and \(m\angle2 = 2x^{\circ}\) into the equation: \((x + 72)+2x=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(x+2x+72 = 180\), which simplifies to \(3x+72=180\).
Subtract 72 from both sides: \(3x=180 - 72\), so \(3x=108\).
Divide both sides by 3: \(x=\frac{108}{3}=36\).

Step3: Find \(m\angle1\)

Substitute \(x = 36\) into \(m\angle1=(x + 72)^{\circ}\). Then \(m\angle1=(36+72)^{\circ}=108^{\circ}\).

Step4: Find \(m\angle2\)

Substitute \(x = 36\) into \(m\angle2=2x^{\circ}\). Then \(m\angle2=2\times36^{\circ}=72^{\circ}\).

Answer:

\(m\angle1 = 108^{\circ}\), \(m\angle2 = 72^{\circ}\)