A triangle has two angles equal to 37 degrees and 53 respectively, show that the triangle is right-angled
To show that the triangle is right-angled, we need to prove that one of the angles measures 90 degrees.
Let's assume angle A measures 37 degrees and angle B measures 53 degrees.
Since a triangle's total angle sum is 180 degrees, we can find the measure of the third angle, angle C, by subtracting the sum of angles A and B from 180 degrees.
Angle C = 180 degrees - (angle A + angle B)
Angle C = 180 degrees - (37 degrees + 53 degrees)
Angle C = 180 degrees - 90 degrees
Angle C = 90 degrees
The measure of angle C is 90 degrees, which means the triangle is right-angled.
To show that the triangle is right-angled, we need to find the third angle and demonstrate that it measures 90 degrees.
Let's denote the two known angles as angle A (37 degrees) and angle B (53 degrees).
Step 1: Find the third angle (angle C) in the triangle using the property that the sum of all angles in a triangle is 180 degrees.
Angle C = 180 degrees - (Angle A + Angle B)
Angle C = 180 degrees - (37 degrees + 53 degrees)
Angle C = 180 degrees - 90 degrees
Angle C = 90 degrees
Step 2: We have found that the third angle in the triangle measures 90 degrees, which is a right angle.
Therefore, we have shown that the triangle is right-angled because it has one angle that measures 90 degrees.
To determine whether a triangle is right-angled or not, we need to look at the angles of the triangle. In a right-angled triangle, one of the angles is always 90 degrees.
In this case, let's assume we have a triangle with angles A, B, and C.
Given that angle A is 37 degrees and angle B is 53 degrees, we can determine the measure of angle C by using the fact that the sum of the angles in a triangle is always 180 degrees.
So, to find angle C, we subtract the sum of angles A and B from 180 degrees:
C = 180 - (A + B)
= 180 - (37 + 53)
= 180 - 90
= 90 degrees
Therefore, angle C is 90 degrees, which means the triangle is right-angled.
In general, to determine if a triangle is right-angled, you can follow these steps:
1. Identify the angles of the triangle.
2. Calculate the sum of the angles.
3. If the sum of the angles is equal to 180 degrees and one of the angles is 90 degrees, then the triangle is right-angled.