Question

In the figure below, find the value of x.

Answer 1

HINT:- Before solving this question, let us know about Straight Angle, Complete angle, and Right Angle.
STRAIGHT ANGLE: An angle whose measure is exactly 180° is called a straight angle. It looks like a straight line.

COMPLETE ANGLE: An angle whose measure is 360° is called a complete angle.

RIGHT ANGLE: An angle whose measure is exactly 90° is called a right angle. It looks like the letter L.

Complete step-by-step answer:
So, as we can see that the figure shown below is a straight line. Therefore, the sum of all of its angles must be 180°.

Therefore, the sum of (x + 3), (x + 20) and (x + 7) will be 180°.
(x + 3) + (x + 20) + (x + 7) = 180°
x + 3 + x + 20 + x + 7 = 180°
3x + 30 = 180°
3x = 180 – 30
3x = 150°
x = \[\dfrac{150}{3}\] = 50°
Therefore, the value of ‘x’ is 50°. (x = 50°).
Now, as we know the value of ‘x’, let us find out the values of the angles too.
(x + 3) = (50 + 3) ° = 53°
(x + 20) = (50 + 20) ° = 70°
(x + 7) = (50 + 7) ° = 57°.
Let us now verify our answer.
(x + 3) + (x + 20) + (x + 7) = 180°
53° + 70° + 57° = 180°
180° = 180°
Hence, verified.

NOTE:- Let us know about Acute, Obtuse and Reflex angles.
ACUTE ANGLE: An acute angle is an angle whose measure is between 0° and 90°.

OBTUSE ANGLE: Obtuse angles are those angles whose measure is more than 90° but less than 180°.

REFLEX ANGLE: A reflex angle is the angle whose measure is more than 180° but less than 360°.