Question

question 4
thuy is correct. fill in the blanks to correctly complete her statement. correct spelling is needed for the first answer.
thuy says, \the polygon must be a triangle, then. with respect to its angles, the triangle is a(n) ____ triangle because if two of its angles are 45° and 46°, the third angle must be ____ °.\

Explanation:

Step1: Find the third - angle of the triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 45^{\circ}\), \(B=46^{\circ}\), and \(C\).
Using the formula \(A + B + C=180^{\circ}\), we can solve for \(C\):
\(C = 180-(45 + 46)\)
\(C=180 - 91\)
\(C = 89^{\circ}\)

Step2: Classify the triangle based on its angles

Since all angles (\(45^{\circ}\), \(46^{\circ}\), and \(89^{\circ}\)) are less than \(90^{\circ}\), the triangle is an acute - angled triangle.

Answer:

acute - angled; \(89\)