Question

1. ok, lets see, suppose that m∠f = (4x - 9)°, m∠g = (3x + 5)°, and m∠h = 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∠f =
°
m∠g =
°
m∠h =
°

Explanation:

Part (a)

Step1: Recall triangle angle sum

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

Step2: Substitute angle expressions

Substitute \(m\angle F=(4x - 9)^\circ\), \(m\angle G=(3x + 5)^\circ\), \(m\angle H = x^\circ\) into the equation: \((4x - 9)+(3x + 5)+x = 180\).

Step1: Simplify the equation

Simplify \((4x - 9)+(3x + 5)+x = 180\). Combine like terms: \(4x+3x+x-9 + 5=180\) → \(8x-4 = 180\).

Step2: Solve for \(x\)

Add 4 to both sides: \(8x=180 + 4=184\). Divide by 8: \(x=\frac{184}{8}=23\).

Step3: Find \(m\angle F\)

Substitute \(x = 23\) into \(4x - 9\): \(4(23)-9=92 - 9 = 83\).

Step4: Find \(m\angle G\)

Substitute \(x = 23\) into \(3x + 5\): \(3(23)+5=69 + 5 = 74\).

Step5: Find \(m\angle H\)

\(m\angle H=x = 23\).

Answer:

\((4x - 9)+(3x + 5)+x = 180\)

Part (b)