The measure of the smaller angle is 88 degrees. Since both angles are a linear pair, this means that they form a 180-degree angle when added together. So, form the equation 5x+7+2x+54=180. Then combine like terms on the left side to get 7x+61=180. Subtract 61 from both sides to get 7x=119. Lastly, divide both sides by 7 to get x=17. To find the smaller angle, substitute 17 for x to get each of the angles' measures. The angle 2x+54 is equivalent to 88 degrees while the angle 5x+7 is equivalent to 92 degrees.