(1) In the following figure, if AB | CD, ZAPQ = 70° and ZPRD = 135º, find x, y and z B P. A Z 70* y 135 с O R D lues of Ar and DO
Answers
Answer:
∠PQR=∠APQ (Alternate angle)
∠PQR=∠APQ (Alternate angle)x=50
∠PQR=∠APQ (Alternate angle)x=50 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlge
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180 ∘ −103
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180 ∘ −103 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180 ∘ −103 ∘ =77
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180 ∘ −103 ∘ =77 ∘
∠PQR=∠APQ (Alternate angle)x=50 ∘ ∠PRQ+∠PRD=180 ∘ ∠PRQ+127 ∘ =180 ∘ ∠PRQ=180 ∘ −127 ∘ =53 ∘ ∠PQR+∠QPR+∠PRQ=180 ∘ (Angle sum property of trianlgex+y+53 ∘ =180 ∘ 50 ∘ +y+53 ∘ =180 ∘ y=180 ∘ −103 ∘ =77 ∘
Answer:
=x+70+135=360
=x+205=360
=x=360-205
=x=155