Question

(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.

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(x+(6x - 7)+(5x - 5)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x + 6x+5x)+(-7 - 5)=180\), which gives \(12x-12 = 180\).

Step3: Solve for \(x\)

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

Step4: Find \(m\angle F\)

Substitute \(x = 16\) into \(5x-5\). So, \(m\angle F=5\times16-5=80 - 5=75^{\circ}\).

Step5: Find \(m\angle G\)

Substitute \(x = 16\) into \(6x-7\). So, \(m\angle G=6\times16-7=96 - 7=89^{\circ}\).

Step6: Find \(m\angle H\)

Since \(x = 16\), \(m\angle H=16^{\circ}\).

Answer:

(a) Equation: \(x+(6x - 7)+(5x - 5)=180\)
(b) \(m\angle F = 75^{\circ}\), \(m\angle G = 89^{\circ}\), \(m\angle H = 16^{\circ}\)