Use Vocabulary in Writing
Shawna drew this picture of three intersecting lines. Use vocabulary terms
to explain how she could determine the value of x.

x° = 43°

Solution:

The lines AD, BE and CF are intersecting lines.

Given m∠AGF = 47°, m∠BGC = 90°, m∠DGE = x°.

To find the value of x°:

Line BE and line CF intersect at the vertex G.

∠BGC and ∠FGE are vertical angles.

Vertical angle theorem:

If two angles are vertically opposite then they are congruent.

By vertical angle theorem, ∠BGC ≅ ∠FGE

⇒ m∠FGE = 90°

Sum of the angles in a straight line = 180°

In line AD,

m∠AGF + m∠FGE + m∠DGE = 180°

⇒ 47° + 90° + m∠DGE = 180°

⇒ 137° + m∠DGE = 180°

⇒ m∠DGE = 180° – 137°

⇒ m∠DGE = 43°

⇒ x° = 43°

Hence the value of x° is 43°.