Answer:
m∠a = 100°
m∠b = 100°
m∠c = 110°
Explanation:
Calculation of m∠a
∠a is an exterior angle of ΔPST .
Therefore m∠a = sum of the interior angles of ΔPST
m∠a = 30 + 70 = 100°
Calculation of m∠c
∠c and ∠PST are supplementary so their measures must add up to 180°
m∠c + 70° = 180° so m∠c = 180 - 70 = 110°
Calculation of m∠b
QRST is a quadrilateral.
The sum of the interior angles of the quadrilateral = 360°
So m∠a + m∠b + 50 + m∠c = 360°
We have already computed ∠a = 100° and ∠c = 110°
So 100 + m∠b + 50 + 110 = 360°
260 + m∠b = 360
m∠b = 360 - 260 = 100°