Question

guys please solve all three questions

Answer 1

I Hope it's help you ☺️✍️

i) angle DCE= angle AEC = 75° ( alternate interior angle )

x° + y° = 180° ....{ linear pair)

75° +x° = 180°

x° = 105°

ii) angle BAE = angle ACD ...{ corresponding angles )

130° = 70° + y°

60° = y°

z°= 70° ...(alt. int. angles)

y° + 70° + x° = 180° ....(linear pair )

60° + 70° +x° =180°

x° = 50°

iii) Let PR is transversal

x° + y° = 115°

Let PQ is transversal

y° + z° = 120°

angle PQR = 180-angle CQP ...(linear pair)

angle PQR = 180-120=>60°= x° (alt. interior angle)

angle PRQ = 180-115 =>65°= y° ( alt. interior angle)

x° + y° = 115°

60° + y° = 115°

y° = 55°

x+y+z=180

60+55+65 =180

180° = 180°

Hence proved..