1.8 Geometry angle pairs

Using the model: Name two adjacent angles

Answer explanation

Using the model: Name two obtuse angles

Answer explanation

An obtuse angle is an angle that measures more than 90° but less than 180°.

It's larger than a right angle but smaller than a straight angle.

For example, if two line segments meet and form an angle that's past a right angle, it's obtuse. You can also think of it as a car seat that's reclined past the 90° upright position. 

Using the model: Name a linear pair whose vertex is F

Using the model: Name two complementary nonadjacent angles

Answer explanation

Non-adjacent complementary angles are two angles that are not adjacent and add up to 90°. They do not share a common vertex or arm.

Answer explanation

1. 1. Supplementary angles add up to 180°.

3. 2. Angle ∠CBF is the angle between segments BC and BF.

4. Angle ∠JBF is the angle between segments BJ and BF.

3. Notice that line BJ and line BC appear to be part of the same straight line when extended. This suggests that angles ∠JBF and ∠CBF are on the same straight line and thus form a linear pair.

4. A linear pair of angles is always supplementary because they lie on a straight line, which measures 180°. In this case, angles ∠JBF and ∠CBF are adjacent angles that share the ray BF and form a straight line.

Find the value of each variable.

Hint: They are supplementary angles.

DO NOT SET THEM EQUAL TO ONE ANOTHER

Mathematical Equivalence

ON

Answer explanation

Find the value of each variable

• x = 46

• y = 18

• x = 18

• y = 46

• x = 3

The measure of an angle's supplement is 76 less than the measure of the angle. Find the measure of the angle and its supplement.

• Angle: 128 degrees,

  Supplement: 52 degrees

• Angle: 104 degrees, Supplement: 76 degrees

• Angle: 52 degrees, Supplement: 128 degrees

• Angle: 152 degrees, Supplement: 28 degrees

Answer explanation

Mathematical Equivalence

OFF

Mathematical Equivalence

ON

Answer explanation