Answer:
x = 16
Explanation:
Exterior Angles of a Triangle
When a side of a triangle is extended past the vertex, the angle that is formed with this side and its adjacent side is called its exterior angle.
The exterior and interior angle by each vertex forms a linear pair, and so their sum is 180°. Therefore, the exterior angles of a triangle sum to 360°.
The given diagram gives expressions for the exterior angles of the triangle ABC.
To calculate the value of x, equate the sum of the exterior angles to 360°, and solve for x.
⇒ (9x + 1)° + (5x + 12)° + (10x - 37)° = 360°
⇒ 9x + 1 + 5x + 12 + 10x - 37 = 360
⇒ 9x + 5x + 10x + 1 + 12 - 37 = 360
⇒ 24x - 24 = 360
⇒ 24x - 24 + 24 = 360 + 24
⇒ 24x = 384
⇒ 24x ÷ 24 = 384 ÷ 24
⇒ x = 16
Therefore, the value of x is 16.