Question

In the given figure AB||DC,angle BDC=35° and angle BAD=80.find x,y and z But in the figure,in place of 30° you mentioned 35°

Answer 1

x=30(alternative interior angles)
30+80+y=180(angle sum property)
110+y=180
y=180-110=70.

Hence , x=30 and y=70

Answer 2

Given,

AB || DC

Angle BDC = 35°

Angle BAD = 80°

To find,

The value of x, y, and z.

Solution,

The values of x, y, and z will be 30°, 70° and 110° respectively.

We can easily solve this problem by following the given steps.

According to the question,

AB || DC

Then, angle ABD and angle BDC are alternate interior angles. So, they will be equal.

Therefore, x = 30° ----- equation 1

We know that sum of all the three angles in a triangle is 180°.

Now in ∆ABD,

Angle DAB + angle ABD + angle ADB = 180°

80 + x + y = 180°

80 + 30 + y = 180° ( Putting the value of x from equation 1)

110 + y = 180°

y = (180-110)° [ Moving 110 from the left-hand side to the right-hand side will result in the change of the sign from plus to minus.]

y = 70°

Now, in ∆ DCB,

Angle DCB + angle CBD + angle BDC = 180°

z + (y-30) + 30 = 180°

z + (70-30) + 30 = 180°

z + 40 + 30 = 180°

z + 70 = 180°

z = (180-70)°

z = 110°

Hence, the values of x, y, and z are 30°, 70° and 110° respectively.