Question

Finding the Interior Angles of Triangles
Two triangles, RPQ and NQP are placed together to create a parallelogram as shown below.

Triangles R P Q and N Q P are connected at side P Q. Angle R is 60 degrees, angle R P Q is 80 degrees, angle N Q P is 80 degrees, and angle Q P N is 40 degrees.

What is the measure of angle PQR?

m∠PQR =
°

What is the measure of angle QNP?

m∠QNP =
°

Answer 1

Triangle RPQ: m∠R + m∠RPQ + m∠PQR = 180°, so 60° + 80° + m∠PQR = 180° ⇒ m∠PQR = 40°.

Triangle NQP: m∠N + m∠NQP + m∠QPN = 180°, so m∠QNP + 80° + 40° = 180° ⇒ m∠QNP = 60°.

m∠PQR = 40°
m∠QNP = 60°