Question

plz help with the 7. question​

Answer 1

Answer:

Angle DAB = Angle BCD(opposite angles in a parallelogram are equal)

125° = 56° + y

125°- 56° = y

69° = y

y = z (Alternate Angles)

69° = z

Angle BAD + Angle DAC = 180°

125° + x = 180° (Adjacent angles in a parallelogram are supplementary)

x = 180° - 125°

x = 55°

Therefore, values of x, y and z are 69°, 69° and 55° respectively.

Answer 2

Answer:

x = 55°, y = 69°, z = 111°

Step-by-step explanation:

56+y = 125° (alternate angles are always equal)

y = 125-56

y = 69°

similarly x = Angle EBC (alternate angles)

Angle CEB = 180 - Angle AEC = 180-z

By angle sum property in triangles,

Sum of all angles = 180°

Angle ECB+Angle EBC+ Angle CEB = 180°

56 + x + 180-z = 180°

x - z = 180-180-56

x - z = -56 -------( eq 1 )

Since AECD is a trapezium which is a quadrilateral,

by angle sum property of Quadrilateral,

sum of all angles = 360°

Angle EAD+ Angle ADC +Angle DCE +Angle CEA=360

125 + x + 69 + z = 360

x + z = 360-125-69

x + z = 166 -------(eq 2)

Solving eq(1) and (2), we get,

x - z = -56

x + z = 166

2x = 110 (-z + z gets cancelled)

x = 110/2 = 55°

On putting the value of x in eq(2), we get,

x + z = 166

55 + z = 166

z = 166 - 55 = 111°