Question

Find m DEF
A. 30
B. 60
C. 90
D.120

Answer 1

120°

Explanation:

It is an equilateral triangle, so all its sides and internal angles measure the same.

The sum of the internal angles of a triangle must be 180°, so each internal angle measures 60°.

The DEF angle is an external angle of that triangle, we can use the next property:

An external angle of a triangle is the sum of the internal angles opposed to it.

The two opposite angles to DEF are DCE and CDE:

DEF = DCE + CDE = 60 ° + 60 ° = 120°

Another way to find this same result is to notice that DEF + DEC total 180° since they form a straight line, and we know that DEC measures 60°

So:

DEF + DEC = 180 °

DEF = 180 ° - DEC

DEF = 180 ° -60 °

DEF = 120 °

Answer 2

The little red lines on each side of the triangle mean that the sides are all equal.

A triangle that has all 3 sides the same is an equilateral triangle.

Because all the sides are identical all 3 inside angles are also identical.

180 / 3 = 60 degrees

The outside angle which is DEF would equal 180 - the inside angle.

DEF = 180 - 60 = 120.

The answer is D.