Answer:
x = 21
m∠DEF = 109°
m∠DBE = 71°
Explanation:
Because CD and DE are congruent, then we can say that this is an isosceles triangle. An isosceles triangle has two congruent sides and the angles opposite them are congruent as well.
This means that m∠DBE is congruent to m∠DEB. So if that is the case, this means that m∠DBA is congruent to m∠DEF.
If you look at the figure, ∠DEF is supplementary to ∠DEB, which means that the sum of their angles are equal to 180°.
Now let's get to solving.
m∠DEF = 4 + 5x
m∠DBE = 7x - 76
m∠DEB ≅m∠DBE
m∠DEF + m∠DEB = 180°
So by substitution:
m∠DEF + m∠DBE = 180°
(4 + 5x) + (7x - 76) = 180°
4 + 5x + 7x - 76 = 180°
Combine like terms:
12x -72 = 180°
add 72 on both sides:
12x - 72 + 72 = 180 + 72
12x = 252
Divide both sides by 12:
12x/12 = 252/12
x = 21
If you need to solve for the angles then:
m∠DEF = 4 + 5x = 4 + 5(21) = 4 + 105 = 109°
m∠DBE = 7x - 76 = 7(21) - 76 = 147 - 76 = 71°