Question

in the triangle, suppose that m∠e=(6x−8)°, m∠f=(5x−4)°, and m∠g=x°. (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. m∠e=88°, m∠f=76°, m∠g=16°.

Explanation:

Part (a)

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle E + m\angle F + m\angle G = 180\).

Step2: Substitute angle measures

Substitute \(m\angle E=(6x - 8)^\circ\), \(m\angle F=(5x - 4)^\circ\), and \(m\angle G = x^\circ\) into the equation: \((6x - 8)+(5x - 4)+x = 180\).

Step1: Simplify the equation

First, simplify \((6x - 8)+(5x - 4)+x = 180\). Combine like terms: \(6x+5x+x-8 - 4=180\), so \(12x-12 = 180\).

Step2: Solve for \(x\)

Add 12 to both sides: \(12x=180 + 12=192\). Then divide by 12: \(x=\frac{192}{12}=16\).

Step3: Find each angle

• \(m\angle G=x = 16^\circ\)
• \(m\angle F=5x - 4=5(16)-4 = 80 - 4=76^\circ\)
• \(m\angle E=6x - 8=6(16)-8 = 96 - 8=88^\circ\)

Answer:

\((6x - 8)+(5x - 4)+x = 180\)

Part (b)