Question

In a quadrilateral ABCD angle A=55° angle B= 85° angle C andD=5:6find angle C and D

Answer 1

Answer:

C = 100° and D = 120°

Step-by-step explanation:

Given In a quadrilateral ABCD

A = 55° and B = 85°

To find : Angle C and D

Let angle C be 5x and angle D be 6x.

Then,

A + B + C + D = 360°

[ Sum of all angles of a quadrilateral is 360° ]

=> C + D = 360° - (A + B)

=> C + D = 360° - (55° + 85°)

=> C + D = 360° - 140°

=> C + D = 220°

=> 5x + 6x = 220°

=> 11x = 220°

=> x = 20°

so, C = 5x = 5 × 20 = 100°

and D = 6x = 6 × 20 = 120°.

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Answer 2

Answer:

Angle C = 100 and Angle D = 120

Step-by-step explanation:

Let angle c and angle d be 5x and 6x respectively.

Now, ATQ,

• A + B + C + D = 360 (ASP of quad.)

• 55 + 85 + 5x + 6x = 360

• 140 + 11x = 360

• 11x = 360 - 140

• 11x = 220

• x = 220/11

• x = 20

Therefore, angle C = 5x = 5 * 20 = 100degree

                  angle D = 6x = 6 * 20 = 120degree