Question

find x in the following figures

Answer 1

GIVEN QUESTION :

Find 'x' in the following figures.

REQUIRED SOLUTION :

(a) We're given with,

Three exterior angles : 125°, 125° & x°.

We know that,

The Sum of all exterior angles of any polygon measures 360°.

So, we will equate all the angle sum to 360° to find out the value of unknown angle,

⇒125° + 125° + x° = 360°

⇒250° + x° = 360°

⇒x° = 360° - 250°

⇒x° = 110°

∴ The measure of x° in figure (a) is 110°.

(b) We're given with,

Three exterior angles : 60°, 90° & 70°.

Here, We also need to find the value of y, in order to get an exterior angle,

⇒y = 180° - 90° (Linear Pair)

⇒y = 90°

Now, We know that,

The Sum of all exterior angles of any polygon measures 360°.

So, we will equate all the angle sum to 360° to find out the value of unknown angle,

⇒60° + 90° + 70° + x + y = 360°

⇒60° + 90° + 70° + x + 90° = 360°

⇒310° + x = 360°

⇒x = 50°

∴ The measure of x° in figure (b) is 50°.

Answer 2

Answer:

(a)

ans = 125° + m = 180° ⇒ m = 180° – 125° = 55° (Linear pair)

125° + n = 180° ⇒ n = 180° – 125° = 55° (Linear pair)

x = m + n (exterior angle of a triangle is equal to the sum of 2 opposite interior 2 angles)

⇒ x = 55° + 55° = 110°

b)

Two interior angles are right angles = 90°

70° + m = 180° ⇒ m = 180° – 70° = 110° (Linear pair)

60° + n = 180° ⇒ n = 180° – 60° = 120° (Linear pair) The figure is having five sides and is a pentagon.

Thus, sum of the angles of pentagon = 540° 90° + 90° + 110° + 120° + y = 540°

⇒ 410° + y = 540° ⇒ y = 540° – 410° = 130°

x + y = 180° (Linear pair)

⇒ x + 130° = 180°

⇒ x = 180° – 130° = 50°