Which statements are true? Select all that apply.

Question

Question 2 options:

Two adjacent angles that make a straight line add up to more than 180 degrees.

The measure of a supplementary angle cannot be acute.

Vertical angles are congruent.

The measure of a complementary angle is acute.

Answer 1

Let's analyze each statement to determine which are true:

1. Two adjacent angles that make a straight line add up to more than 180 degrees.

   • This statement is false. Two adjacent angles on a straight line always add up to exactly 180 degrees.

2. The measure of a supplementary angle cannot be acute.

   • This statement is false. A supplementary angle refers to two angles whose measures add up to 180 degrees. One of the angles can be acute (less than 90 degrees) while the other is obtuse (greater than 90 degrees).

3. Vertical angles are congruent.

   • This statement is true. Vertical angles are formed when two lines intersect, and they are always equal in measure.

4. The measure of a complementary angle is acute.

   • This statement is true. Complementary angles are two angles whose measures add up to 90 degrees, and since neither angle can exceed 90 degrees, they must both be acute.

Based on this analysis, the true statements are:

• Vertical angles are congruent.
• The measure of a complementary angle is acute.