Question

angle 1 and 2 are supplementary. if ( mangle1 = 7x + 7 ) and ( mangle2 = x - 9 ). determine the value of x and the measure of each angle. ( x = ) type your answer... ( mangle1 = ) type your answer... ( mangle2 = ) type your answer...

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180\). Substitute \(m\angle1 = 7x + 7\) and \(m\angle2=x - 9\) into the equation: \((7x + 7)+(x - 9)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+x+7 - 9=180\), which simplifies to \(8x-2 = 180\).

Step3: Solve for \(x\)

Add \(2\) to both sides: \(8x-2 + 2=180 + 2\), so \(8x=182\). Then divide both sides by \(8\): \(x=\frac{182}{8}=\frac{91}{4}=22.75\).

Step4: Find \(m\angle1\)

Substitute \(x = 22.75\) into \(m\angle1=7x + 7\). \(m\angle1=7\times22.75+7=159.25 + 7=166.25^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 22.75\) into \(m\angle2=x - 9\). \(m\angle2=22.75-9 = 13.75^{\circ}\).

Answer:

\(x = 22.75\)
\(m\angle1=166.25^{\circ}\)
\(m\angle2 = 13.75^{\circ}\)