Answer to Question #182152 in Geometry for Reiana

Question

 Imagine line AB is parallel with line CD , line EF intersects line AB at point G and line CD at point H. If the m∠AGE=80°, what would be the measurement of ∠DHF? *

1 point

A. 80 degrees

B. 100 degrees

C. 110 degrees

D. 120 degrees

Answer 1

AB || CD and EF is their transversal

So

m$\angle AGE = m\angle CHG$ -------(1)

[ since they are corresponding angles and corresponding angles with respect to parallel lines become equal .]

Again

$m\angle CHG = m\angle DHF$ -------(2)

[ Since they are vertically opposite angles and vertically opposite angles are always equal]

From (1) and (2) we can write

$m\angle AGE = m\angle DHF$

So

$m\angle DHF = 80°$

Therefore option A is correct