Question

what type of triangle is this? all triangles have an angle sum of 180°. triangle with angles 57° and 35° a acute triangle b obtuse triangle c right triangle

Explanation:

Step1: Calculate the third angle

The sum of angles in a triangle is \(180^\circ\). Given two angles \(35^\circ\) and \(57^\circ\), the third angle \(x\) is calculated as \(x = 180^\circ - 35^\circ - 57^\circ\).
\[x = 180 - 35 - 57 = 88^\circ\]

Step2: Classify the triangle

An acute triangle has all angles less than \(90^\circ\), an obtuse triangle has one angle greater than \(90^\circ\), and a right triangle has one angle equal to \(90^\circ\). Here, all angles (\(35^\circ\), \(57^\circ\), \(88^\circ\)) are less than \(90^\circ\), so it's an acute triangle. But wait, wait, no—wait, 88 is less than 90, but wait, maybe I miscalculated? Wait, 35 + 57 is 92, 180 - 92 is 88? Wait, no, 35 + 57 is 92? 35 + 57: 35 + 50 is 85, plus 7 is 92. Then 180 - 92 is 88. Wait, but 88 is acute. But wait, the options: A is acute, B is obtuse, C is right. Wait, but maybe I made a mistake. Wait, no, 35 + 57 is 92, 180 - 92 is 88. All angles are acute (less than 90), so it's an acute triangle? But wait, the original problem—wait, maybe the triangle has a right angle? Wait, no, the given angles are 35 and 57. Wait, maybe I miscalculated. Wait, 35 + 57: 35 + 57 = 92. 180 - 92 = 88. So all angles are less than 90, so acute. But wait, the options: A is acute, B is obtuse, C is right. So the answer should be A? Wait, but maybe I made a mistake. Wait, let me check again. 35 + 57 = 92. 180 - 92 = 88. Yes, 88 is less than 90. So all angles are acute, so it's an acute triangle. But wait, the problem's triangle—wait, the diagram shows a right triangle? Wait, no, the diagram has a right angle? Wait, the triangle in the diagram looks like a right triangle, but the angles given are 35 and 57. Wait, maybe the diagram is misleading. Wait, according to the angle sum, 35 + 57 + x = 180, so x = 88. So all angles are acute, so it's an acute triangle. So the correct option is A.

Wait, but maybe I messed up. Wait, 35 + 57 is 92, 180 - 92 is 88. So all angles are less than 90, so acute. So the answer is A.

Answer:

A. Acute triangle