Answer:
m∠E = 57º
Explanation:
We can use the isosceles triangle theorem to determine that angle E is congruent to angle D, since side DF is congruent to side EF.
This means that:
m∠E = m∠D
m∠E = (4x + 1)º
Now, we can solve for x using the fact that the interior angles of a triangle sum to 180º.
m∠D + m∠E + m∠F = 180º
↓ substituting the given angles measures (in terms of x)
(4x + 1)º + (4x + 1)º + (5x - 4)º = 180º
↓ grouping like terms
(4x + 4x + 5x)º + (1 + 1 - 4)º = 180º
↓ combining like terms
13xº - 2º = 180º
↓ adding 2º to both sides
13xº = 182º
↓ dividing both sides by 13º
x = 14
With this x value, we can now solve for m∠E using its definition in terms of x.
m∠E = (4x + 1)º
↓ plugging in solved x value
m∠E = (4(14) + 1)º
m∠E = (56 + 1)º
m∠E = 57º