What is the measure of E

The measure of angle E is:

m∠E = 80°

Step-by-step explanation:

Given

The triangle ΔDEF

It is stated that 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.

Given

m∠GDE = 10°

As the right-angle triangle, ΔDEG lies at the right-angle G.

So, 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°

100 + m∠E = 180°

m∠E = 180° - 100

m∠E = 80°

Therefore,

The measure of angle E is: m∠E = 80°

step-by-step explanation: