Question

in the triangle, suppose that ( mangle f = (4x - 9)^circ ), ( mangle g = (3x + 5)^circ ), and ( mangle h = x^circ ).
(a) write an equation to find ( x ). make sure you use an \=\ sign in your answer.
equation: (square)
(b) find the degree measure of each angle.
( mangle f = square^circ )
( mangle g = square^circ )
( mangle h = square^circ )

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 measures

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

Step1: Simplify the equation

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

Step2: Solve for \(x\)

Add 4 to both sides: \(8x = 184\). Divide by 8: \(x = 23\).

Step3: Find \(m\angle F\)

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

Step4: Find \(m\angle G\)

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

Step5: Find \(m\angle H\)

Substitute \(x = 23\) into \(m\angle H = x\): \(23\).

Answer:

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

Part (b)