In ΔEFG, m, angle, E, equals, left parenthesis, 7, x, plus, 12, right parenthesis, degreesm∠E=(7x+12)

Question

∘
, m, angle, F, equals, left parenthesis, 6, x, minus, 9, right parenthesis, degreesm∠F=(6x−9)
∘
, and m, angle, G, equals, left parenthesis, 2, x, plus, 12, right parenthesis, degreesm∠G=(2x+12)
∘
. What is the value of x, question markx?
Answer

Answer 1

In any triangle, the sum of the interior angles is 180 degrees. Therefore, we can set up the following equation using the given expressions for the angles in triangle \( \triangle EFG \):

\[ m\angle E + m\angle F + m\angle G = 180 \]

Substituting the expressions for the angles:

\[ (7x + 12) + (6x - 9) + (2x + 12) = 180 \]

Now, combine the terms:

1. Combine the \( x \) terms: \[ 7x + 6x + 2x = 15x \]

2. Combine the constant terms: \[ 12 - 9 + 12 = 15 \]

Now, we can rewrite the equation:

\[ 15x + 15 = 180 \]

Next, subtract 15 from both sides:

\[ 15x = 165 \]

Now, divide by 15:

\[ x = 11 \]

Thus, the value of \( x \) is

\[ \boxed{11} \]