How to find an angle in a right triangle - Basic Geometry

First, know that all the angles in a triangle add up to 180 degrees.

Each triangle has 3 angles. Thus, we have the sum of three angles as shown:

where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we'll call that angle A. The other known angle is 90 degrees and we'll call this angle B. Thus, we have

Simplify and solve for C.

A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.

The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:

The remaining choice is correct:

The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.

Let = first angle and = second angle

So the equation to solve becomes or

Thus, the first angle is and the second angle is .

So the smaller angle is

The interior angles of a triangle always add up to 180 degrees. We are given angle and since this is indicated to be a right triangle we know angle is equal to 90 degrees. Thus we know 2 of the 3 and can determine the third angle.

Angle is equal to 55 degrees.

All of these statements are false.

A right triangle can be equilateral.

False: An equilateral triangle must have three angles that measure each.

One leg can be longer than the hypotenuse.

False: Each leg is shorter than the hypotenuse.

A right triangle can have an obtuse angle.

False: Both angles of a right triangle that are not right must be acute.

The measures of the angles of a right triangle can total .

False: The measures of any triangle total .

The formula to find all the angles of a triangle is:

To solve for the measure of angle , we plug in the values of and . Since angle is a right angle, we know the measure will be .

The internal angles of a triangle always add up to 180 degrees, and it was given that the triangle was right, meaning that one of the angles measures 90 degrees.

This leaves 90 degrees to split evenly between the two remaining angles as was shown in the question.

Therefore, each of the two equal angles has a measure of 45 degrees.

The angles of a triangle all add up to .

This means that .

Using the fact that 90 is half of 180, we can figure out that the missing angle, x, plus 34 adds to the remaining 90, and we can just subtract

.

The angles of a triangle add together to 180 degrees. We already know that one of the angles is 90 degrees, so we can subtract 90 from 180: the other 2 angles have to add to 90 degrees.

We can now subtract to get x:

The angles of a triangle always add to 180 degrees.

That means that in this case,

since we know that the right angle is 90 degrees.

There are a few ways we can move on from here, but one is to simplify this equation:

now subtract 145

The equation to find the area of a triangle is:

In this problem, both the base and the height are 6in. By plugging in the numbers, we get

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures degrees.

Thus, for the triangle in question,