Three angles fit around a point. Two of the angles are 112^circ and 57^circ a) Work out the size of the third angle. Give your answer in degrees ()

Sure, let's take it step by step.<br /><br />Given information:<br />We have three angles fitting around a point, let’s denote these by the capital letters A, B, and C. We know two of these angles. Angle A is 112° and angle B is 57°, given in the LaTeX format as \(112^{\circ}\) and \(57^{\circ}\) respectively.<br /><br />Task:<br />We need to work out the size of the third angle C. We'll determine this in degrees (\(^{\circ}\)).<br /><br />Step 1: Recall the sum of angles around a point<br />Remember that the sum of angles around a point is equal to 360°. In terms of LaTeX format, this is usually shown as a circle known as a "full turn," represented by \(360 \, ^{\circ}\).<br /><br />Step 2: Sum up the given angles<br />First we should sum up the given angles. These include angle A which equals 112° and angle B which equals 57°. The sum will lead to\(A + B = 112 + 57 ^{\circ} =169^{\circ}\).<br /><br />Step 3: Find the third angle<br />Lastly, since we know the total sum of a full turn (360°) and the sum of \(A + B=169 ° \), we can get the size of the third angle (C) by subtraction as follows: \( C = 360 ^{\circ} - 169^{\circ}\).<br /><br />So, according to algebraic norms, \(C = 360 - 169 = 191 ^{\circ} \). Thus, the third angle C is equal to \(191^{\circ}\). <br /><br />So, we can conclude: <br />The size of the third angle, C, is \(\boxed{191^{\circ}} \).