Question

in triangle DEF, DE=EF and G is the midpoint of EF. if the measure of GDE=10 what is the measure of E?

Answer 1

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Answer:

The measure of angle E is:

m∠E = 80°

Step-by-step explanation:

Given

The triangle ΔDEF

m∠GDE = 10°

DE = EF

G = midpoint of EF

To Determine

m∠E =?

Solving

As DE=EF and G is the midpoint of EF.

• It means the midpoint G has converted the triangle into two equal right-angles triangles ΔDEG and ΔDFG with the right-angle at G.

So, the right angle G is m∠DGE = 90°

as

• m∠GDE = 10°

• m∠DGE = 90°

• m∠E = ?

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

m∠GDE + m∠DGE  + m∠E = 180°

10° + 90° + m∠E = 180°

m∠E = 180°  - 10 - 90

m∠E = 80°

Therefore, we conclude that the measure of angle E is:

• m∠E = 80°