Question

In ΔDEF, start overline, D, F, end overline DF is extended through point F to point G, m, angle, D, E, F, equals, left bracket, x, plus, 20, right bracket, degrees m∠DEF=(x+20) ∘ , m, angle, F, D, E, equals, left bracket, 3, x, plus, 12, right bracket, degrees m∠FDE=(3x+12) ∘ , and m, angle, E, F, G, equals, left bracket, 6, x, plus, 4, right bracket, degrees m∠EFG=(6x+4) ∘ . Find m, angle, E, F, G, .m∠EFG.

Answer 1

The measure of angle EFG in triangle DEF is 90.4 degrees.

Step-by-step explanation:

To find the measure of angle EFG in triangle DEF, we can set up an equation using the given angle measures.

We know that the sum of the angles in a triangle is 180 degrees.

So, we have the equation:

(x + 20) + (3x + 12) + (6x + 4) = 180

Combining like terms and solving for x, we get:

10x + 36 = 180

10x = 144

x = 14.4

Now we can substitute x back into the angle measures to find the measure of angle EFG:

m∠EFG = 6x + 4

m∠EFG = 6(14.4) + 4

m∠EFG = 86.4 + 4

m∠EFG = 90.4 degrees.