Question

in 8 & 9, use the following figure.

1. what is the value of ( x ) ?

14 19 32 24

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(3(x + 7)=x+63\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(3x+21=x + 63\).

Step3: Subtract \(x\) from both sides

\(3x - x+21=x - x+63\), which simplifies to \(2x+21 = 63\).

Step4: Subtract 21 from both sides

\(2x+21-21=63 - 21\), so \(2x=42\).

Step5: Divide both sides by 2

\(x=\frac{42}{2}=21\). Wait, there is a mistake. Let's check again.

Wait, the correct exterior - angle formula: The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
The exterior angle is \(63^{\circ}\), and the two non - adjacent interior angles are \(x\) and \(3(x + 7)\). So \(x+3(x + 7)=63\).
Expand: \(x + 3x+21=63\).
Combine like terms: \(4x+21 = 63\).
Subtract 21 from both sides: \(4x=63 - 21=42\).
Divide by 4: \(x = 14\).

Answer:

14