Points What is the value of y? 54 A. 73° B. 126° C. 63°
The Correct Answer and Explanation is:
To solve for the value of angle yyy in the given triangle, we apply the Triangle Angle Sum Theorem, which states that the sum of the interior angles in any triangle is always 180 degrees.
From the image, we see that two angles are provided:
- One angle is labeled as 54∘54^\circ54∘
- The other is labeled as 63∘63^\circ63∘
We are asked to find the third angle, yyy, of the triangle.
Step-by-Step Calculation:
Sum of angles in triangle=180∘\text{Sum of angles in triangle} = 180^\circSum of angles in triangle=180∘y=180∘−54∘−63∘y = 180^\circ – 54^\circ – 63^\circy=180∘−54∘−63∘y=180∘−117∘=63∘y = 180^\circ – 117^\circ = 63^\circy=180∘−117∘=63∘
Final Answer:
C. 63∘63^\circ63∘
Explanation
In any triangle, the sum of all three interior angles is always 180 degrees. This fundamental rule is known as the Triangle Angle Sum Theorem. It applies universally to all triangles, whether they are right, acute, or obtuse.
In the given image, we are provided with two angle measures: 54∘54^\circ54∘ and 63∘63^\circ63∘. To find the missing angle yyy, we subtract the sum of the known angles from 180 degrees:180∘−(54∘+63∘)=63∘180^\circ – (54^\circ + 63^\circ) = 63^\circ180∘−(54∘+63∘)=63∘
This tells us that the measure of angle yyy must be 63∘63^\circ63∘ to satisfy the rule that the angles of a triangle add up to 180 degrees.
Understanding and applying the Triangle Angle Sum Theorem is essential not just in geometry, but also in real-world contexts such as engineering, architecture, and design. When constructing any triangular structure, such as a truss or support beam, knowing the angle relationships ensures the stability and accuracy of the construction.
Additionally, identifying missing angles through subtraction is a basic yet powerful tool in geometry. It allows students and professionals to determine unknown parts of figures using limited information, which is a common scenario in problem-solving.
Therefore, the correct answer to the question, based on the given angle measurements and applying the triangle sum theorem, is C. 63∘63^\circ63∘.
