Question

Find the measure of ZA, ZB, ZC and ZD in the parallelogram. if A-3a° , B- 6a°, C- 4a°​

Answer 1

Answer:

∠A = 96.93°

∠B  =  83.07°

∠C = 96.93°

∠D =  83.07°

Step-by-step explanation:

Given,

∠CAB = 3a°

∠B = 6a°

∠BCD = 4a°

To Find :-

Measure of angles ∠A , ∠B , ∠C , ∠D

How To DO :-

We can observe that , ∠CAB  , ∠B , ∠BCD forms a triangle So by using the properties of the triangle we need to equate their sum to 180° , then we can find the value of 'a' and we can find those real values and we need to find those values of the angles.

Formula Required :-

1) Sum of three angles in a triangle = 180°

2) Sum of two consecutive angles in a parallelogram = 180°

3) Opposite angles are equal in a parallelogram

Solution :-

∠CAB + ∠B + ∠BCD = 180°

[ ∴  Sum of three angles in a triangle = 180°]

3a° + 6a° + 4a° = 180°

13a° = 180°

a° = 180°/13°

∴ ∠B = 6a°

= 6 × 180/13

= 83.07° [ Approx]

∴ ∠B = ∠D =  83.07°

[ ∴ Opposite angles are equal in a parallelogram]

∠A + ∠B = 180°

∠A + 83.07° = 180°

∠A = 180° - 83.07°

∴ ∠A = 96.93°

→∠A = ∠C = 96.93°

∴ ∠A , ∠B , ∠C , ∠D = 96.93° , 83.07° , 96.93° , 83.07°.