Question

the measures of two angles of a triangle are given. find the measure of the third angle.
54° 8, 96° 29

the measure of the third angle is □° □.
(simplify your answer. type a whole number.)

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\), which is \(179^\circ 60'\) (since \(1^\circ = 60'\)).

Step2: Add the two given angles

First, add the degrees: \(54^\circ+96^\circ = 150^\circ\). Then add the minutes: \(8'+29' = 37'\). So the sum of the two angles is \(150^\circ 37'\).

Step3: Subtract from total

Subtract \(150^\circ 37'\) from \(179^\circ 60'\). Subtract degrees: \(179^\circ - 150^\circ = 29^\circ\). Subtract minutes: \(60' - 37' = 23'\). So the third angle is \(29^\circ 23'\)? Wait, no, wait. Wait, \(180^\circ\) is \(179^\circ 60'\). Wait, \(180^\circ - 150^\circ 37' = (179^\circ - 150^\circ)+(60' - 37') = 29^\circ + 23' = 29^\circ 23'\)? But wait, let's check again. Wait, \(54 + 96 = 150\), \(8 + 29 = 37\). Then \(180 - 150 = 30\), but we have to subtract the minutes. So \(180^\circ = 179^\circ 60'\). So \(179^\circ 60' - 150^\circ 37' = (179 - 150)^\circ + (60 - 37)' = 29^\circ 23'\). Wait, but the problem says "Type a whole number" for each? Wait, maybe I made a mistake. Wait, no, the sum of angles in a triangle is \(180^\circ\). So two angles are \(54^\circ 8'\) and \(96^\circ 29'\). Let's convert them to decimal degrees to check. \(54 + 8/60 \approx 54.1333^\circ\), \(96 + 29/60 \approx 96.4833^\circ\). Sum is \(54.1333 + 96.4833 \approx 150.6166^\circ\). Then \(180 - 150.6166 \approx 29.3833^\circ\). Convert \(0.3833^\circ\) to minutes: \(0.3833\times60 \approx 23'\). So it's \(29^\circ 23'\). Wait, but the problem says "Type a whole number" for each box. So degrees is 29, minutes is 23.

Answer:

\(29^\circ\ 23'\)