Question

in the figure, ( mangle 1 = (8x)^circ ) and ( mangle 2 = (x - 18)^circ ).
(a) write an equation to find ( x ). make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
( mangle 1 = ) ( ^circ )
( mangle 2 = ) ( ^circ )

Explanation:

Step1: Use the linear - pair property

Angles \( \angle1\) and \( \angle2\) form a linear pair. The sum of the measures of angles in a linear pair is \(180^{\circ}\). So, the equation is \(m\angle1 + m\angle2=180^{\circ}\). Substituting \(m\angle1=(8x)^{\circ}\) and \(m\angle2=(x - 18)^{\circ}\), we get \(8x+(x - 18)=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation \(8x+(x - 18)=180\). Combine like terms: \(8x+x-18 = 180\), which gives \(9x-18 = 180\). Add \(18\) to both sides: \(9x-18 + 18=180 + 18\), so \(9x=198\). Divide both sides by \(9\): \(x=\frac{198}{9}=22\).

Step3: Find \(m\angle1\)

Substitute \(x = 22\) into \(m\angle1=(8x)^{\circ}\). Then \(m\angle1=8\times22^{\circ}=176^{\circ}\).

Step4: Find \(m\angle2\)

Substitute \(x = 22\) into \(m\angle2=(x - 18)^{\circ}\). Then \(m\angle2=(22-18)^{\circ}=4^{\circ}\).

Answer:

(a) Equation: \(8x+(x - 18)=180\)
(b) \(m\angle1 = 176^{\circ}\), \(m\angle2 = 4^{\circ}\)