## Exercise 3.1 Part 2

Question 6: Find the angle measures x in the following figures.

Solution: We know that, angle sum of a quadrilateral = 360⁰
So, 50° + 130° + 120°+ x = 360°
Or, 300°+ x = 360°
Or, x = 360°- 300°= 60°

Question 6 (b)

Solution:

We know that, angle sum of a quadrilateral = 360⁰
So, 90° + 60°+ 70°+ x = 360°
Or, 220° + x = 360°
Or, x = 360°- 220°= 140°

Question 6 (c)

Solution:Solution

We know that angle sum of a pentagon = 540o
110° + 120° + 30° + x + x = 540°
Or, 260° + 2x = 540°
Or, 2x = 540° - 260° = 280°
Or, x = 280°÷2 = 140°

Question 6 (d)

Solution:Solution: Angle sum of a pentagon = (5 – 2) xx 180⁰ = 3 xx 180⁰ = 540⁰
Since, it is a regular pentagon, thus, its angles are equal
So, x + x + x + x + x = 540°
Or, 5x = 540°
Or, x = 540°÷5 = 108°

Question 7:

Solution:

We know that angle sum of a triangle = 180⁰
Thus, 30⁰ + 90⁰ + C = 180⁰
Or, 120⁰ + C = 180⁰
Or, C = 180⁰ – 120⁰
Or, C = 60⁰
Now, y = 180° - C
Or, y = 180° - 60° = 120°
Similarly, z = 180°- 30° = 150°
Similarly, x = 180° - 90° = 90°
Hence, x + y + z = 90° + 120° + 150°= 360°

Alternate method: We know that sum of external angles of a polygon = 360⁰
Hence, x + y + z = 180°

Solution:

We know that angle sum of a quadrilateral = 360⁰
A + 60° + 80° + 120° = 360°
Or, A + 260° = 360°
Or, A = 360° - 260° = 100°
Hence, w = 180° - 100° = 80°
Similarly, x = 180° - 120° = 60°
Similarly, y = 180° - 80° = 100°
Similarly, z = 180° - 60° = 120°
Hence, x + y + z + w = 60° + 100° + 120° + 80° = 360°

Alternate method: We know that sum of external angles of a polygon = 360⁰
Hence, x + y + z + w = 360°