Question

solve and find x,y and z​

Answer 1

Answer:

x=55,y=35,z=90

Step-by-step explanation:

In given figure AB || CD and EF is a transversal

is a transversalso

is a transversalso(1)

is a transversalso(1)angle APQ=angle CQF (alternate angles)

is a transversalso(1)angle APQ=angle CQF (alternate angles)30°+y=65°

is a transversalso(1)angle APQ=angle CQF (alternate angles)30°+y=65°y=65°-30°

is a transversalso(1)angle APQ=angle CQF (alternate angles)30°+y=65°y=65°-30°y=35°

is a transversalso(1)angle APQ=angle CQF (alternate angles)30°+y=65°y=65°-30°y=35°(2)

angle APQ + angle CQP =180° (interior angles)

(30+y)° + (25+z)°=180°

30°+35°+25°+z=180°

90°+z=180°

z=180°-90°

z=90°

(3)

In ∆RQP,

angle x +angle y +angle z=180° (sum of measures of angles of triangle in 180°)

x+y+z=180°

x+35°+90°=180°

x=180°-125°

x=55°