Question

Three angles of a quadrilateral are 60°, 75° and 100°. Find the fourth angle. Also, find all the four external angles.

Answer 1

Given: Quadrilateral PQRS with ∠SPQ = 60°, ∠PQR = 75° and ∠QRS = 100°

We know that the sum of the angles of a quadrilateral is 360°.

⇒ ∠SPQ + ∠PQR + ∠QRS + ∠RSP = 360°

⇒ 60° + 75° + 100° + ∠RSP = 360°

⇒ 235° + ∠RSP = 360°

⇒∠ RSP = 360° − 235°

= 125°

The measures of the external angles of a quadrilateral can be calculated using the property of linear pair.

We know that the sum of the measures of angles forming a linear pair is 180°.

⇒ ∠QRS + ∠QRX = 180°

⇒ ∠QRS = 180° − 100°

= 80°

Similarly, ∠RQP + ∠PQW = 180°

⇒ ∠PQW = 180° − 75°

= 105°

∠SPQ + ∠SPZ = 180°

⇒ ∠SPZ = 180° − 60°

= 120°

∠RSY + ∠RSP = 180°

⇒∠ RSY = 180° − 125°

= 55°

Thus, the measures of the external angles of the given quadrilateral are 80°, 105°, 120° and 55°.