Find the value of x in the given triangle. One interior angle is x degrees, another...
Check the final answer first, then review the worked steps.
Problem
Find the value of x in the given triangle. One interior angle is x degrees, another interior angle is 85 degrees. An exterior angle is 135 degrees.
Answer
50
Step-by-step solution
- Identify the exterior angle: The image shows an exterior angle of $135^\circ$. An exterior angle and its adjacent interior angle form a linear pair, meaning they add up to $180^\circ$.
- Calculate the adjacent interior angle: Let the adjacent interior angle be $y$. Then, $y + 135^\circ = 180^\circ$. Subtracting $135^\circ$ from both sides gives $y = 180^\circ - 135^\circ = 45^\circ$.
- Apply the angle sum property of a triangle: The sum of the interior angles of a triangle is always $180^\circ$. In this triangle, the interior angles are $x^\circ$, $85^\circ$, and the angle we just calculated, $45^\circ$.
- Set up the equation: So, we have the equation: $x^\circ + 85^\circ + 45^\circ = 180^\circ$.
- Solve for x: Combine the known angles: $x^\circ + 130^\circ = 180^\circ$. Subtract $130^\circ$ from both sides: $x^\circ = 180^\circ - 130^\circ$. Therefore, $x^\circ = 50^\circ$.