Theorem 1: Examples

Examples on Theorem 1
Published on ginnyent on 16th May, 2019.
Example 1
The angles of a triangle are x, 2x and 3x. Find the value of x in degrees.
Solution
Recall what theorem 1 says.
It now follows that x + 2x + 3x = 1800
Collecting like terms we have:
6x = 1800
Therefore x = 1800/6
= 300
x = 300, 2x = 600 and 3x = 900. You can see that the triangle is a right-angled triangle.

Example 2
An isosceles triangle is such that each of the base angles is twice the vertical angle. Find the angles of the triangle.
Solution
Let’s make a sketch. See the diagram below.

From the diagram, we have assumed the vertical angle to be a, and the two base angles to be 2a.
We know from theorem 1 that the sum of the angles in a triangle is 1800.

Therefore, we will sum the three angles and equate it to 1800
a + 2a + 2a = 1800
Collecting like terms, we have:
5a = 1800
a = 1800/5
a = 360
2a =
The angles of the triangle are therefore: 360 , 720 and 720

Example 3
In a right-angled triangle, one of the acute angles is 200 greater than the other. Find the angles of the triangle.

    Solution
    Let’s look at the diagram below.

    From the diagram, we have the angles of the triangle to be: 900, a, and a+200
    We already know from theorem 1 that the sum of the angles in a triangle is 1800
    Therefore, we will equate the sum of the angles to 1800
    900+ a + (a+ 200) = 1800
    Collecting like terms, we have:
    1100 + 2a = 1800
    2a = 1800 – 1100
    2a = 700
    a = 700/2
    = 350
    a = 350
    a + 200 = 550
    Therefore the angles of the triangle are: 900, 550 and 350

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