Question

From the figure, what is the value of x?

• A. \( 50^\circ \)
• B. \( 120^\circ \)
• C. \( 60^\circ \)
• D. \( 70^\circ \)

Hint:

\textbf{Exterior Angle Theorem.} The Exterior Angle Theorem is a fundamental concept in geometry related to triangles. It states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Answer 1

The Correct Option is D

In the given figure, we have a triangle ABC. The angle at vertex A is given as \( 50^\circ \). The exterior angle at vertex C, \( \angle ACD \), is given as \( 120^\circ \). We need to find the value of the interior angle at vertex B, which is labeled as \( x \). According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two opposite interior angles. In triangle ABC, the exterior angle at C (\( \angle ACD \)) is equal to the sum of the interior angles at A (\( \angle BAC \)) and B (\( \angle ABC \)). So, we have: $$ \angle ACD = \angle BAC + \angle ABC $$ Substituting the given values: $$ 120^\circ = 50^\circ + x $$ To find the value of \( x \), we can rearrange the equation: $$ x = 120^\circ - 50^\circ $$ $$ x = 70^\circ $$ Therefore, the value of \( x \) is \( 70^\circ \).