Question

in the figure, ( mangle 1 = (x + 72)^circ ) and ( mangle 2 = (3x)^circ )
(a) write an equation to find ( x ). make sure you use the \=\ sign in your answer.
equation: (square)
(b) find the degree measure of each angle.
( mangle 1 = square^circ )
( mangle 2 = square^circ )

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle1\) and \(\angle2\) are supplementary (they form a linear - pair), \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1=(x + 72)^{\circ}\) and \(m\angle2=(3x)^{\circ}\), the equation is \((x + 72)+3x=180\).
Simplify the left - hand side: \(x+3x + 72=180\), which gives \(4x+72 = 180\).
Subtract 72 from both sides: \(4x=180 - 72\), so \(4x=108\).
Divide both sides by 4: \(x=\frac{108}{4}=27\).

Step2: Find \(m\angle1\)

Substitute \(x = 27\) into \(m\angle1=(x + 72)^{\circ}\). Then \(m\angle1=(27+72)^{\circ}=99^{\circ}\).

Step3: Find \(m\angle2\)

Substitute \(x = 27\) into \(m\angle2=(3x)^{\circ}\). Then \(m\angle2=(3\times27)^{\circ}=81^{\circ}\).

Answer:

(a) Equation: \(x + 72+3x=180\) (or \(4x+72 = 180\))
(b) \(m\angle1 = 99^{\circ}\), \(m\angle2 = 81^{\circ}\)