the exterior angle equals the the sum of the two opposite interior angles
6x = x + 40 + 3x + 10
I can get angles inside triangle to equal 180 but when I check for the extended point it does not add up to straight line 180
6x = x + 40 + 3x + 10
To find the measure of angle CAB, we can set up an equation using the fact that the sum of the angles in a triangle is 180 degrees.
So we have x + 40 + 3x + 10 + 6x = 180.
Simplifying the equation, we get 10x + 50 = 180.
Subtracting 50 from both sides gives us 10x = 130.
And finally, dividing both sides by 10, we get x = 13.
Therefore, the measure of angle CAB is x + 40, which is 13 + 40 = 53 degrees.
I hope that clears things up and puts a smile on your face, even if Triangle ABC is feeling a little twisted!
1. The sum of the angles in a triangle is 180 degrees.
2. Let's denote the measure of angle CAB as "a". Therefore, angle ACB can be expressed as (3a + 10) degrees and angle CBD as 6a degrees.
3. As triangle ABC is extended to point D, we consider the extended line. The sum of the angles on a straight line is 180 degrees.
4. So, we have a + (3a + 10) + 6a = 180. We combine like terms.
5. Simplifying the equation, we get 10a + 10 = 180.
6. Subtracting 10 from both sides of the equation, we have 10a = 170.
7. Dividing both sides of the equation by 10, we find that a = 17.
Therefore, the measure of angle CAB is 17 degrees.
Let's call angle CAB as "a", angle ACB as "b", and angle CBD as "c".
We are given the following information:
- Angle CAB = x + 40
- Angle ACB = 3x + 10
- Angle CBD = 6x
To find the measure of angle CAB, we need to solve for "x" first. We can use the fact that the angles in a triangle add up to 180 degrees.
So, we can write the equation as:
x + 40 + 3x + 10 + 6x = 180
Simplifying the equation, we have:
10x + 50 = 180
Subtracting 50 from both sides:
10x = 130
Dividing both sides by 10:
x = 13
Now, we can substitute the value of "x" back into the equation for angle CAB:
Angle CAB = x + 40
Angle CAB = 13 + 40
Angle CAB = 53
So, the measure of angle CAB is 53 degrees.