Question

GEOMETRY 100 POINTS

Find the x​

Answer 1

x = 18

Explanation:

There are 2 ways to do this :

1) Method 1 :

sum of exterior angles of a triangle = 360

⇒ (9x - 31) + (4x + 33) + (7x - 2) = 360

⇒ 20x = 360

⇒ x = 360/20

⇒ x = 18

2) Method 2:

Since the three lines are straight lines, the interior angles of the triangle are given by:

∠CDE = 180 - (9x - 31) = 211 - 9x

∠DEC = 180 - (4x + 33) = 147 - 4x

∠ECD = 180 - (7x - 2) = 182 - 7x

The sum of angles in a triangle = 180

∠CDE + ∠DEC + ∠ECD = 180

⇒ 211 - 9x + 147 - 4x + 182 - 7x = 180

⇒ 540 - 20x = 180

⇒ 20x = 540 - 180

⇒ 20x = 360

⇒ x = 360/20

⇒ x = 18