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Solve for x: Triangle with 120°, 80° Angles
Published on September 29, 2024
Geometry
Find the missing angle 'x' in a triangle where one angle is 80 degrees and the exterior angle adjacent to the 80-degree angle is 120 degrees. The solution is x = 140 degrees.
Question
Answer
Let’s break down this problem step-by-step.
1. Identify the Unknown Angle
We need to find the value of ‘x’, which represents an unknown angle.
2. Use Angle Properties
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Straight Angle: The angle formed by a straight line is 180 degrees. Notice that the 120-degree angle and one of the interior angles of the triangle form a straight angle. Let’s call this interior angle ‘a’. We can write the equation:120° + a = 180°
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Solving for ‘a’: Subtract 120° from both sides of the equation:a = 60°
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Angles in a Triangle: The sum of all interior angles in a triangle is always 180 degrees. We now know two angles inside the triangle: 60° and 80°. Let’s use this to find the third angle, which we’ll call ‘b’:60° + 80° + b = 180°
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Solving for ‘b’: Combine the known angles and subtract from 180°:140° + b = 180°
b = 40° -
Finding ‘x’: Finally, notice that ‘x’ and angle ‘b’ (40°) also form a straight angle:x + 40° = 180°
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Solving for ‘x’: Subtract 40° from both sides:x = 140°
Answer: x = 140°