Question

1. (19x - 18)° (7x + 1)° (10x - 9)°

Explanation:

1. Recall the exterior - angle property of a triangle:

• The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles.
• In the given triangle, the exterior angle is \((19x - 18)^{\circ}\), and the two non - adjacent interior angles are \((7x + 1)^{\circ}\) and \((10x-9)^{\circ}\).

1. Set up the equation:

• According to the exterior - angle property, we have the equation \(19x-18=(7x + 1)+(10x-9)\).
• First, simplify the right - hand side of the equation:
• Combine like terms on the right - hand side: \((7x + 1)+(10x-9)=7x+10x + 1-9=17x-8\).
• So our equation becomes \(19x-18 = 17x-8\).
• Then, solve for \(x\):
• Subtract \(17x\) from both sides of the equation: \(19x-17x-18=17x-17x - 8\).
• This simplifies to \(2x-18=-8\).
• Add 18 to both sides: \(2x-18 + 18=-8 + 18\).
• We get \(2x = 10\).
• Divide both sides by 2: \(x=\frac{10}{2}=5\).

Answer:

\(x = 5\)