Question

in the triangle below, \\( \angle g \\) is a right angle. suppose that \\( m \angle f = ( 2 x + 9 ) ^ { \circ } \\) and \\( m \angle h = ( 3 x + 6 ) ^ { \circ } \\).
(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 \angle f = \square ^ { \circ } \\)
\\( m \angle h = \square ^ { \circ } \\)
\\( m \angle g = \square ^ { \circ } \\)

Explanation:

Step1: Use the triangle angle - sum property

In a right - triangle, the sum of the interior angles is \(180^{\circ}\), and since \(\angle G = 90^{\circ}\), we have \((2x + 9)+(3x + 6)+90=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation:

$$
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$$

Step3: Find \(m\angle F\)

Substitute \(x = 15\) into the expression for \(\angle F\): \(m\angle F=2x + 9=2\times15+9=30 + 9=39^{\circ}\)

Step4: Find \(m\angle H\)

Substitute \(x = 15\) into the expression for \(\angle H\): \(m\angle H=3x + 6=3\times15+6=45 + 6=51^{\circ}\)

Answer:

(a) Equation: \((2x + 9)+(3x + 6)+90=180\)
(b) \(m\angle G = 90^{\circ}\), \(m\angle F=39^{\circ}\), \(m\angle H = 51^{\circ}\)