Question

determine an expression for \\(x\\) in terms of \\(a\\) based on the following diagram:

\\(x = 5a - 3\\)
\\(x = -a + 5\\)
\\(x = -5a + 3\\)
\\(x = a - 5\\)

Explanation:

Identify the given angles

We are given a triangle with two interior angles:

• One interior angle is \(3a - 4\).
• Another interior angle is \(2a + 1\).
• The exterior angle opposite to these two interior angles is \(x\).

Apply the Exterior Angle Theorem

Using the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

$$ x = (3a - 4) + (2a + 1) $$

Simplify the expression

Combine the like terms to find \(x\) in terms of \(a\):

$$ x = 3a + 2a - 4 + 1 $$

$$ x = 5a - 3 $$

Answer:

• (A) \(x = 5a - 3\) (Correct answer)
• (B) \(x = -a + 5\)
• (C) \(x = -5a + 3\)
• (D) \(x = a - 5\)