Find the value of
in the triangle shown below.
103° 33°
Find the value of
in the triangle shown below.
103° 33°
The Correct Answer and Explanation is:
To find the unknown angle xx in a triangle when two other angles are given, we apply a fundamental property of Euclidean geometry: the sum of the interior angles in any triangle is always exactly 180 degrees.
In this case, the triangle has two known angles, 103° and 33°. According to the triangle angle sum rule:
x+103∘+33∘=180∘x + 103^\circ + 33^\circ = 180^\circ
Now add the two known angles:
103∘+33∘=136∘103^\circ + 33^\circ = 136^\circ
Subtract this sum from 180° to find xx:
x=180∘−136∘=44∘x = 180^\circ – 136^\circ = 44^\circ
So, the missing angle xx is 44 degrees.
Explanation
Understanding triangles is a key concept in geometry and this problem demonstrates how to apply one of the most foundational rules. The sum of the interior angles in a triangle will always equal 180 degrees. This rule works regardless of whether the triangle is acute, obtuse, or right. It arises from the way lines intersect and form supplementary angles on a flat plane.
In the given triangle, two angles are known: one is 103° and the other is 33°. Since all three interior angles together must total 180°, we can find the missing angle by subtracting the sum of the known angles from 180°. The addition of 103° and 33° gives 136°. When we subtract this from 180°, we get 44°, which is the measure of the unknown angle.
This type of problem is common in both academic settings and practical applications. Architects, engineers, and graphic designers often rely on triangular measurements to ensure precision in their projects. Knowing how to calculate a missing angle quickly and accurately helps in constructing stable structures and creating accurate models.
Even in fields like computer graphics and navigation, triangle geometry plays an essential role. Trigonometric functions often require knowledge of angle measures and triangle properties. Therefore, mastering this fundamental technique builds a strong foundation for more advanced mathematical problem solving and real-world applications.
