Question

Solve for the unknown angles. Justify your answers with steps (do not just provide answers)

Answer 1

∠ LKQ = 102°, ∠ PNQ = 117°

Explanation:

∠ LKQ = 180° - 78° = 102° ( adjacent angles on a straight line )

∠ KQN = 180° - 67° = 113° ( adjacent angles on a straight line )

The sum of the interior angles of a quadrilateral = 360° , then

∠ LNQ = 360° - (102 + 113 + 82)° = 360° - 297° = 63°

Then

∠ PNQ = 180° - 63° = 117° ( adjacent angles on a straight line )

Answer 2

PNQ=117

LKQ=102

Explanation:

LKQ=180-78=102

KQN=180-67=113

LNQ=360-82-102-113=63

PNQ=180-63=117