Question

In a trapezium ABCD, angle A is three times of angle D. Find the value of angle A. a)120° b)135° c)90° d)145°​

Answer 1

Answer:

Let angle D be x.

So angel A is 3x.

A+D=180 (because consecutive interior angles add upto 180)

x+3x=180

4x = 180

x = 45°

so D = 45°

So angle A would be 45×3= 135°

so option B is correct

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Answer 2

Given,

Trapezium is ABCD.

$\[\angle A = 3\angle D\]$----------(1)

Solution,

Consider the trapezium is ABCD. It's angles are $\[\angle A,\angle B,\angle C,\angle D\]$

Consider angle A and D are adjacent angles.

Know that the sum of adjacent angles of a trapezium is $\[180^\circ \]$

$\[\angle A + \angle D = 180^\circ \]$---------(2)

Put value of angle D from equation 1.

$\[ \Rightarrow \angle A + \frac{{\angle A}}{3} = 180^\circ \]$

$\[ \Rightarrow \frac{{4\angle A}}{3} = 180^\circ \]$

$\[ \Rightarrow \angle A = 135^\circ \]$

Hence the value of angle A is $\[135^\circ \]$

The correct option is (b), i.e. $\[135^\circ \]$