Given ΔMNO, find the measure of ∠LMN.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
38°
52°
76°
104°
76°
Since segment MN and NO are marked congruent, it means they are equal in length, making triangle MNO an isosceles triangle. This means that angle MNO and angle MON are equal. Since angle MON and angle NOP form a straight angle (180°), we can determine that angle MON is 76°.
Since angle LMN is an exterior angle to triangle MNO, its measure is equal to the sum of the two remote interior angles, which are equal in an isosceles triangle. This means that angle LMN is also 76°.