Question

Use the diagram to answer the question

Answer 1

Answer:

$m\angle EFG=52^{o}$

Step-by-step explanation:

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

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.

$m\angle EFG=m\angle IGF+m\angle EJG$

Upon substituting our given values we will get,

$m\angle EFG=13^{o}+39^{o}$

$m\angle EFG=52^{o}$

Therefore, measure of angle EFG is 52 degrees.