Arithmetic in Geometry Examples

Suppose SK bisects LN. What is the measurement of LN?

Since SK bisects LN at point M, we know LM and MN both measure 4 units. That means LN has a total measurement of 8 units.

What is the measurement of ∠ROS?

∠ROS and ∠MON are vertical angles, so they're congruent. That means ∠ROS measures 32°, the same as ∠MON.

What is the measurement of ∠NOT?

Angles ∠MON, ∠NOT, and ∠SOT together split up line MS, so their measurements must add up to 180°. Since m∠MON = 32 and m∠SOT = 20, that means ∠NOT must measure 180 – 32 – 20 = 128°.

If ∠JMO measures 43°, what is the measurement of ∠JML?

Since ∠LMO is a right angle, we know that angles ∠JMO and ∠JML are complementary. Since they add up to 90°, that means m∠JML = 90 – 43 = 47°.