Question

Derek, Ben, and Nate are stargazing. They spot three bright stars that form a triangle.
They find the approximate angles of the two sides of the triangle to be 98° and 36° but argue over the third angle.
Derek thinks the third angle is 54°, Ben thinks it's 78°, while Nate thinks it's 46°.
Who is correct?

• A. Derek
• B. Nate
• C. Ben
• D. None of them

Answer 1

The correct option is B Nate

Let the unknown angle be x.

We know that the sum of three angles of a triangle is 180°.

So,
x + 98° + 36° = 180°
⇒ x = 180° – (98° + 36°)
⇒ x = 180° – 134° = 46°

Hence, the third angle is 46°, and Nate is correct.