Answer:
x = 20 and the triangle is a scalene obtuse
Explanation:
Creating an equation to solve for x
Angles in a triangle add up to 180 degrees.
This means that 6x - 5 + x + 45 = 180
Solving for x using basic algebra
6x - 5 + x + 45 = 180
==> combine like terms
7x + 40 = 180
==> subtract 40 from both sides
7x = 140
==> divide both sides by 7
x = 20
Finding the values of each angle by plugging in x
Angle 1 = 6x - 5
==> plug in x = 20
Angle 1 = 6(20) - 5
==> multiply 6 and 20
Angle 1 = 120 - 5
==> subtract 5 from 120
Angle 1 = 115
Angle 2 = x
x = 20 so Angle 2 = 20
And we are given the other angle which has a measure of 45 degrees
So this triangle has angle measures of 20 , 115 and 45
Classifying the triangle by sides
To classify the triangle by sides we use the following
- All equal sides = Equilateral
- Two equal sides = Isosceles
The triangle has no equal sides so it is a scalene triangle
Classifying the triangle by angles.
To classify the triangle by angles we use the following
- If it has all angles less than 90 then its a acute triangle
- If it has an angle with 90 degrees then its a right triangle
- If it has an angle with a measure of more than 90 degrees then its an obtuse triangle
Here, the triangle has angle measures of 115, 45 and 20
There is an angle with a measure of more than 90 degrees therefore it is an obtuse triangle
So we can conclude that x = 20 and this triangle is a scalene obtuse