Question

In the trapezium BEST,the measure of angle B=64°,angle E=64°.Angle BTS is equals to_______ degree of angle.​

Answer 1

Answer:

116°

Step-by-step explanation:

Answer 2

SOLUTION:

Given:

BEST is  trapezium, in which

∠B = 64°

∠E = 64°

To be found

∠BTS = ?

So,

Lets know the properties of a trapezium first,

• The two opposite sides are parallel. [In the attached imaged BE is parallel to TS i.e. BE║TS]

• So, as two opposite sides are parallel, so the adjacent angles (i.e opposite to parallel) make 180 as sum. So, in the figure, trapezium BEST, ∠B + ∠T = 180° and also, ∠E + ∠S = 180° .

So,

∠B + ∠T = 180°

And given, ∠B = 64°

⇒ 64° + ∠T = 180°

⇒ ∠T = 180° - 64°

⇒ ∠T = 116°

Hence,

∠T (i.e.  ∠BTS) = 116°

- - - - -

Verification:

Sum of all four interior angles of trapezium should be 360°.

We can get ∠S by similar method of ∠T

We will get ∠S = 180 - 64 = 116°

Now,

∠B + ∠E + ∠S + ∠T

= 64° + 64° + 116° + 116°

= 128° + 232°

= 360°  checked