Question

Question 10In the figure below, line pline q.nepDIfZ DEH = 97 which of the following angles will equal 83?A ZOBEB. HEDC. BEFD. ZABGE ZGBCE. ZDEBG. FEHH. ZEBA

Answer 1

A. ∠CBE

D. ∠ABG

F. ∠DEB

G. ∠FEH

1) Examining those parallel lines cut by a transversal one, we have all these angles, so we can state:

Given m∠DEH = 97º

Then m∠FEH = 180º -97º Since ∠FEH and ∠DEF are supplementary

m∠FEH= 83º

The corresponding angle to ∠FEH and therefore congruent is angle:

∠GBA= 83º

The vertical angle to FEH is also congruent

∠DEB = 83º

And the vertical angle to ∠GBA is also congruent to

∠CBE=83

2) So visually we have these angles congruent to 83º

Alternate interior angles (∠FEH and ∠GBA), Vertical Angles (∠FEH and ∠DBE, ∠GBA and ∠CBE) , and Corresponding angles (∠FEH and ∠CBE), are always congruent to each other.

So the answers are:

A. ∠CBE

D. ∠ABG ( or GBA)

F. ∠DEB

G. ∠FEH