Question

In figure 3.37, determine the value of x.​

Answer 1

Answer

We are asked to find the value of x from the figure.

As we observe we can see that in the figure all the angles are around a point.

The sum of all the angles around a point  is equal to three hundred and sixty degree.

$\implies$ 3x + 3x + x + 150° = 360°

$\implies$7x + 150°  = 360°

$\implies$ 7x = 360°  - 150°

$\implies$ 7x = 210°

$\implies \sf x = \dfrac{210}{7}$

$\implies$ x = 30°

Let Us Verify

Before verification , we must find out the values of the angles .

$\bigstar$ 3x = 3 × 30 = 90°

$\bigstar$  x = 30°

So, all the Angles around the point are :- 150° , 90° , 90° , 30°

Now, Let us see if the sum of these angle add to 360°.

Sum of all the angles = 150° + 90° +90° +30° = 360°

Hence , verified that the answer is correct.

Answer 2

Answer:

$3x + 3x = 180°$

$6x = 180°$

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

$x = 30°$

second way of finding

$150° + x = 180$

$x = 180° - 150°$

$x = 30°$