Question

working with interior angles of a triangle
manipulate the triangle so ∠a measures 14° and ∠b measures 62°.
which statement is true about ∠c?
the angle is a right angle.
the angle is acute.
the angle is obtuse.
the angle does not make a straight line with the other two.

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles in a triangle is \(180^\circ\). So, \(\angle A + \angle B + \angle C = 180^\circ\).

Step2: Substitute given angles

Given \(\angle A = 14^\circ\) and \(\angle B = 62^\circ\), substitute into the formula: \(14^\circ + 62^\circ + \angle C = 180^\circ\).

Step3: Calculate \(\angle C\)

First, sum \(\angle A\) and \(\angle B\): \(14^\circ + 62^\circ = 76^\circ\). Then, solve for \(\angle C\): \(\angle C = 180^\circ - 76^\circ = 104^\circ\).

Step4: Classify \(\angle C\)

An obtuse angle is greater than \(90^\circ\) and less than \(180^\circ\). Since \(104^\circ > 90^\circ\), \(\angle C\) is obtuse.

Answer:

The angle is obtuse.