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Use the diagram to answer the question

Line m is parallel to line p. M angle HEF IS 39 degrees. And m IGF is 13 degrees. Find the m EFG. Explain in detail how you know you are correct. I WILL MARK THE BRAINLIEST

Use the diagram to answer the question Line m is parallel to line p M angle HEF IS 39 degrees And m IGF is 13 degrees Find the m EFG Explain in detail how you k class=

Respuesta :

Answer:

[tex]m\angle EFG=52^{o}[/tex]

Step-by-step explanation:

We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].

Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.

We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.

We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]

Upon substituting our given values we will get,

[tex]m\angle EFG=13^{o}+39^{o}[/tex]

[tex]m\angle EFG=52^{o}[/tex]

Therefore, measure of angle EFG is 52 degrees.

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