Answer:
The value of x is 3
Step-by-step explanation:
In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.
In the given triangle
∵ The angle of measure (7x + 26)° is an exterior angle
∵ The angles of measures (10x + 11)° and (x + 3)° are the opposite
interior angles to this angle
→ By using the rule above
∴ (10x + 11)° + (x + 3)° = (7x + 26)°
→ Add the like terms in the left side
∵ (10x + x) + (11 + 3) = 7x + 26
∴ 11x + 14 = 7x + 26
→ Subtract 7x from both sides
∵ 11x - 7x + 14 = 7x - 7x + 26
∴ 4x + 14 = 26
→ Subtract 14 from both sides
∵ 4x + 14 - 14 = 26 - 14
∴ 4x = 12
→ Divide both sides by 4 to find x
∵ [tex]\frac{4x}{4}[/tex] = [tex]\frac{12}{4}[/tex]
∴ x = 3
∴ The value of x = 3
