Question

not drawn to scale

what is the value of \\(x\\)?

\\(22^\circ\\)
\\(79^\circ\\)
\\(136^\circ\\)
\\(158^\circ\\)

Explanation:

Identify the vertical angle

The angle labeled \(22^\circ\) and the interior angle \(\angle BAC\) of \(\triangle ABC\) are vertical angles formed by two intersecting lines. Vertical angles are equal in measure.

$$ m\angle BAC = 22^\circ $$

Apply the triangle angle sum theorem

Using the Triangle Angle Sum Theorem, the sum of the interior angles of \(\triangle ABC\) must equal \(180^\circ\).

$$ m\angle BAC + m\angle B + m\angle C = 180^\circ $$

Substitute the known values and solve for x

Substitute the angle measures into the equation:

$$ 22^\circ + x + x = 180^\circ $$

$$ 22 + 2x = 180 $$

$$ 2x = 158 $$

$$ x = 79^\circ $$

Answer:

• (A) \(22^\circ\)
• (B) \(79^\circ\) (Correct answer)
• (C) \(136^\circ\)
• (D) \(158^\circ\)