Question

Find the measure of each of the three angles on a straight line if two of them are
equal and third is twice of both.​

Answer 1

The sum of all angles in a straight line will always be equal to 180°. These angles are called a linear pair.

Let the first angle on the straight line be x .

Then, the second angle = x

The third angle :-

$= x + x \times 2$

$= 2x \times 2$

$= 4x$

Thus, the third angle =4x

The sum of all three of these angles = 180°

This can be written in an equation as :-

$= x + x + 4x = 180°$

$= 2x + 4x = 180°$

$= 6x = 180°$

$= x = \frac{180}{6}$

$= x = 30$

Which means :-

the measure of the first angle =30°

The measure of the second angle =30°

The measure of the third angle :-

$= (30 + 30)2$

$= 60 \times 2$

$= 120°$

Thus, the measure of the third angle =120°

Now, let us check whether or not we have found out the correct value of each angle by placing 30 in the place of x:-

$= 30 + 30 + (30 + 30)2 = 180$

$= 60 +(60)2= 180$

$= 60 + 120 = 180$

$= 180 = 180$

$\tt{LHS=RHS }$

As the left hand side of the equation is equivalent to the right hand side of the equation, we can conclude that we have found out the correct measure of each of the angles in this straight line.

Therefore, the measure of the first angle=30° , the measure of the second angle= 30° and the measure of the third angle=120°