Question

Please help me with this, thank you. (points!!)

Answer 1

51.5 degrees (not much information, so use the answer at your own risk)

Explanation:

Assuming that the lines DE and FE are congruent, this means that the triangle is isosceles. From this, we can deduce that the other two angles are equal. The angles can be represented by x for now.

All the angles add up to 180, and there are two unknown but equal angles, so it can be written as:

77 + 2x = 180

↑

(The two unknown angles, which are equal)

Now we just need to isolate x by subtracting 77 from both sides.

2x = 103

x = 51.5

Since x equals both of the angles, it also equals angle EDF

Answer 2

m∠EDF = 51.5°

Explanation:

Given:

• DE = EF
• m∠DEF = 77°

To find:

• m∠EDF = ?

Solution:

Since base side DE is equal to EF, so ∆ DEF is an isoceles triangle

We have:

Base angle of isoceles triangle are equal.

In this case:

m∠DFE and m∠EDF are base angles.

So,

m∠EDF = m∠DFE = x (let)

Since

Sum of interior angles of a triangle is 180°

So,

m∠EDF + m∠DFE + m∠DEF = 180°

x + x + 77° = 180°

2x = 180° - 77°

2x = 103°

`\sf x = (103)/(2)`

x = 51.5°

Therefore, m∠EDF = 51.5°