Chapter 3 Understanding Quadrilaterals Ex 3.3 Solutions
Question - 11 : - Find the measure of тИаP and тИаS if SP || RQ ? in Fig 3.34. (If you find mтИаR, is there more than one┬аmethod to find mтИаP?)
Answer - 11 : -
тИаP + тИаQ = 180┬░ (angles on the same side of transversal)
тЗТ тИаP + 130┬░ = 180┬░
тЗТ тИаP = 180┬░ тАУ 130┬░ = 50┬░
also, тИаR + тИаS = 180┬░ (angles on the same side of transversal)
тЗТ 90┬░ + тИаS = 180┬░
тЗТ тИаS = 180┬░ тАУ 90┬░ = 90┬░
Thus, тИаP = 50┬░ and тИаS = 90┬░
Yes, there are more than one method to find mтИаP.
PQRS is a quadrilateral. Sum of measures of all angles is 360┬░.
Since, we know the measurement of тИаQ, тИаR and тИаS.
тИаQ = 130┬░, тИаR = 90┬░ and тИаS = 90┬░
тИаP + 130┬░ + 90┬░ + 90┬░ = 360┬░
тЗТ тИаP + 310┬░ = 360┬░
тЗТ тИаP = 360┬░ тАУ 310┬░ = 50┬░
Question - 12 : - Find mтИаC in Fig 3.33 if AB || DC ?
Answer - 12 : -
mтИаC + mтИаB = 180┬░ (angles on the same side of transversal)
тЗТ mтИаC + 120┬░ = 180┬░
тЗТ mтИаC = 180┬░- 120┬░ = 60┬░