Triangle ABC is extended to point D Angle CAB =x+40 Angle ACB = 3x +10 angle CBD = 6x what is measure of angle CAB?
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
the exterior angle equals the the sum of the two opposite interior angles
6x = x + 40 + 3x + 10
Well, it seems like Triangle ABC is going through a bit of an identity crisis, extending itself and all. But don't worry, I'm here to help!
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!
To find the measure of angle CAB, we can set up an equation based on the information given. Let's proceed step-by-step:
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.
To find the measure of angle CAB, we need to use the fact that the angles in a triangle add up to 180 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.