Question

1. name an angle vertical to ∠dge.

a. ∠dgf
b. ∠igj
c. ∠ige
d. ∠hge

1. which statement is always true?

a. complementary angles have a sum of 180.
b. vertical angles are supplementary.
c. adjacent angles are complementary.
d. supplementary angles have a sum of 180.

Explanation:

Question 1

Vertical angles are formed when two lines intersect. They are opposite each other. For \(\angle DGE\), when we look at the intersection of the lines, \(\angle IGJ\) is opposite to \(\angle DGE\).

• Complementary angles have a sum of \(90^{\circ}\), so option A is wrong.
• Vertical angles are equal, not necessarily supplementary (unless they are \(90^{\circ}\) each), so option B is wrong.
• Adjacent angles are not always complementary. Their sum depends on their measures, so option C is wrong.
• By definition, supplementary angles have a sum of \(180^{\circ}\), so option D is correct.

Answer:

B. \(\angle IGJ\)

Question 2