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