Question

In triangle DEF, EF is a bisector. If m∠DEF=3x+1 and 2⋅m∠DEG=5.2+19, find x and the measure of m∠DEG.

Said x = ___________

Measure of m∠DEGm∠DEG: ___________

A) 20
B) 18
C) 15
D) 25

Answer 1

To find x and the measure of angle DEG in triangle DEF, we can use the angle bisector theorem. By setting up an equation with the ratios of the lengths and measures of the angles, we can solve for x and DEG. In this case, x is 19 and DEG is 24.2 degrees.

Step-by-step explanation:

To find the value of x and the measure of angle DEG, we need to use the angle bisector theorem. According to the theorem, if EF is a bisector, then the ratio of the lengths of DE to DF is equal to the ratio of the measures of angles DEF to FED. We can set up the following equation: DE/DF = (3x+1)/(180-(3x+1)).

Simplifying this equation, we get DE/DF = (3x+1)/(179-3x). Since EF is a bisector, DE/DF = ED/EF. Substituting the values, we get (3x+1)/(179-3x) = 1/2.

Cross multiplying, we get 2(3x+1) = 179-3x. Simplifying this equation gives us 6x+2 = 179-3x. Combining like terms, we get 9x = 177, which means x = 19. Angle DEG is 5.2+19 = 24.2 degrees.