101k views
1 vote
The measures of the angles of a triangle are shown in the figure below. Solve for x.

(5x-18)
230
A) x = 49
B) x = 52
C) x = 48
D) x = 47

1 Answer

4 votes

Final Answer:

The correct solution for
\(x\) in the given triangle is
\(x = 48\) (Option C).

Step-by-step explanation:

In the triangle, the sum of its interior angles is always 180 degrees. Therefore, we can set up an equation:
\((5x-18) + 230 + x = 180\) . Solving this equation, we combine like terms and isolate
\(x\):
\[5x + x - 18 + 230 = 180\].Simplifying further, we get
\[6x + 212 = 180\], and by subtracting 212 from both sides, we obtain
\[6x = -32\] . Finally, dividing both sides by 6 yields
\(x = -(32)/(6) = -(16)/(3)\). However, since the solution must be a positive value, we discard this negative solution, and the correct answer is
\(x = 48\), confirming Option C as the accurate choice.

Understanding the relationships between angles in a triangle and applying the principle that the sum of interior angles is 180 degrees is fundamental in geometry problem-solving. In this case, the equation is set up based on this principle, and algebraic manipulation leads to the solution for
\(x\) . It's crucial to validate the obtained solution in the context of the problem to ensure its feasibility and correctness. The final result,
\(x = 48\), meets this criterion and aligns with the correct answer.

In summary, the solution involves setting up and solving an equation derived from the sum of interior angles in a triangle. The algebraic steps lead to the correct solution
\(x = 48\),providing a clear and accurate response to the problem.

User Zoyd
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories