Question

1. find the missing angle and classify both triangles.

65°
35°
60°
50°
?

Explanation:

Step1: Find the missing angle of the first triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the missing angle be \(x\).
\(x + 60^{\circ}+65^{\circ}=180^{\circ}\)
\(x=180^{\circ}-(60^{\circ} + 65^{\circ})\)
\(x = 55^{\circ}\)
Since all angles (\(55^{\circ},60^{\circ},65^{\circ}\)) are less than \(90^{\circ}\), it is an acute triangle.

Step2: Find the missing angle of the second triangle

First, find the adjacent angle to \(50^{\circ}\) in the first - triangle. Since the sum of angles on a straight line is \(180^{\circ}\), the adjacent angle \(y = 180^{\circ}-55^{\circ}-50^{\circ}\) (wait, no, correct way: the angle adjacent to the \(50^{\circ}\) (formed by the two triangles) and the first - triangle's \(55^{\circ}\) and the second - triangle's angles.

The sum of angles in the second triangle: Let the missing angle be \(z\).
We know one angle is \(35^{\circ}\), and using the linear - pair concept (the angle adjacent to the first - triangle's calculated \(55^{\circ}\) and \(50^{\circ}\) part: the angle adjacent to the first - triangle's angles at the common vertex.

The angle at the common vertex (let's call it \(a\)): \(a=180^{\circ}-(60^{\circ}+65^{\circ})=55^{\circ}\) (from the first triangle sum). Then, for the second triangle, using the sum of angles in a triangle (\(180^{\circ}\))
\(z=180^{\circ}-35^{\circ}-(180^{\circ}-55^{\circ}-50^{\circ})\) (no, correct: the sum of angles in a triangle is \(180^{\circ}\). The angle adjacent to the first - triangle's angles (at the common side) is \(180^{\circ}-(60^{\circ}+65^{\circ}) = 55^{\circ}\). Then for the second triangle, we know one angle is \(35^{\circ}\), and using the fact that the sum of angles in a triangle is \(180^{\circ}\)
Another approach:
The sum of angles in a triangle is \(180^{\circ}\).
For the second triangle:
Let the missing angle be \(A\)
We know that \(A+35^{\circ}+(180^{\circ}-(60^{\circ}+65^{\circ})) = 180^{\circ}\)
First, \(60^{\circ}+65^{\circ}=125^{\circ}\), the angle adjacent to them (on a straight line) is \(180^{\circ}-125^{\circ} = 55^{\circ}\)
Then \(A=180^{\circ}-35^{\circ}-55^{\circ}\)
\(A = 90^{\circ}\)

Since one angle (\(90^{\circ}\)) is a right - angle, it is a right - triangle.

Answer:

The missing angle of the first triangle is \(55^{\circ}\) (acute triangle), and the missing angle of the second triangle is \(90^{\circ}\) (right - triangle).