Question

19

Answer 1

The measure of each angles  are m∠F = 46°, m∠D = 32°, m∠E = 102°.

What is angle?

An angle in plane geometry is a shape created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is where the word "angle" comes from. The common endpoint of two rays is known as the vertex, and the two rays are known as sides of an angle.

The angle that lies in the plane need not be in Euclidean space. Angles are referred to as dihedral angles if they are produced by the intersection of two planes in a space other than Euclidean. The symbol "" is used to represent an angle.

We have given that Δ DEF has

m∠D = m∠F - 14

And

m∠E = 10 + 2(m∠F)

We know that that sum of all angels in a triangle is 180°, So

m∠D + m∠E  +  m∠F = 180°

Substituting the values we get

(m∠F - 14) + (10 + 2(m∠F)) + m∠F = 180°

m∠F - 14 + 10 + 2m∠F +m∠F

4(m∠F) - 4 = 180

4(m∠F) = 180 + 4

4(m∠F)  = 184

(m∠F)  = 46°

m∠D = 46° - 14

m∠D = 32°

m∠E = 10 + 2(m∠F)

m∠E = 10 + 2( 46°)

m∠E = 10 + 92°

m∠E = 102°

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