Question

In the adjoining figure ABCD is a trapezium. If angle A : angle D=5:7, B= (3x+11)° and angle C= 5x-31)°, then find all the angles of the trapezium​

Answer 1

Step-by-step explanation:

From the given figure, ABCD is a trapezium ∠A:∠D=5:7,∠B=(3x+11) ∘

and ZC=(5x−31) ∘

Then, ∠B+∠C=180 ∘

... [because co - interior angle]

(3x+11) ∘

+(5x−31) ∘

=180 ∘

3x+11+5x−31=180 ∘

8x−20=180 ∘

By transposing we get,

8x=180 ∘

+20

8x=200 ∘

x=200 ∘

/8

x=25 ∘

Then, ∠B=3x+11

=(3×25)+11

=75+11

=86 ∘

∠C=5x−31

=(5×25)−31

=125−31

=94 ∘

let us assume the angles ∠A=5y and ∠D=7y

We know that, sum of co - interior angles are equal to 180 ∘

.

∠A+∠D=180 ∘

5y+7y=180 ∘

12y=180 ∘

y=180

∘

/12

y=15 ∘

Then, ∠A=5y=(5×15)=75 ∘

∠D=7y=(7×15)=105 ∘

Therefore, the angles are ∠A=75 ∘

,∠B=86 ∘

,∠C=94 ∘

and ∠D=105 ∘