The measures of two angles of a triangle are given. Find the measure of the third angle.
$57.4^{\circ}, 74^{\circ}$
The measure of the third angle is
(Simplify your answer. Type an integer or a decimal.)
Final Answer: The measure of the third angle is \(\boxed{48.6^{\circ}}\).
Step 1 :Given the measures of two angles of a triangle are \(57.4^{\circ}\) and \(74^{\circ}\).
Step 2 :The sum of the angles in a triangle is always \(180^{\circ}\).
Step 3 :Therefore, to find the measure of the third angle, we need to subtract the sum of the given angles from \(180^{\circ}\).
Step 4 :Let's denote the third angle as \(\text{angle3}\).
Step 5 :So, \(\text{angle3} = 180 - (57.4 + 74)\).
Step 6 :Calculating the above expression gives \(\text{angle3} = 48.599999999999994^{\circ}\).
Step 7 :However, the result is not exactly a round number due to the precision of floating point arithmetic. We can round the result to the nearest tenth to get a cleaner answer.
Step 8 :So, the rounded measure of the third angle is \(48.6^{\circ}\).
Step 9 :Final Answer: The measure of the third angle is \(\boxed{48.6^{\circ}}\).