Question

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

Explanation:

Step1: Usar la suma de ángulos en un triángulo

La suma de los ángulos internos de un triángulo es \(180^\circ\). Entonces, \(m\angle E + m\angle F + m\angle G = 180\). Sustituyendo los valores: \((x + 4) + (5x + 8) + 6x = 180\).

Step2: Resolver la ecuación para \(x\)

Combinar términos: \(x + 4 + 5x + 8 + 6x = 180\) → \(12x + 12 = 180\). Restar 12: \(12x = 168\). Dividir por 12: \(x = 14\).

Step3: Calcular cada ángulo

• \(m\angle E = x + 4 = 14 + 4 = 18^\circ\)
• \(m\angle F = 5x + 8 = 5(14) + 8 = 70 + 8 = 78^\circ\)
• \(m\angle G = 6x = 6(14) = 84^\circ\)

Answer:

(a) Equation: \((x + 4) + (5x + 8) + 6x = 180\)
(b) \(m\angle E = 18^\circ\), \(m\angle F = 78^\circ\), \(m\angle G = 84^\circ\)