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
solved
To find the measure of angle CAB, you can use the fact that the sum of the interior angles of a triangle is always 180 degrees. However, in this case, we are provided with an extended line segment CD, which intersects the triangle ABC.
Let's start by finding the sum of the interior angles of triangle ABC. We have:
Angle CAB = x + 40
Angle ACB = 3x + 10
The sum of these two angles can be represented as:
(x + 40) + (3x + 10)
Simplifying the expression, we get:
4x + 50
Now, we also have angle CBD = 6x. This angle is not a part of triangle ABC but rather an exterior angle formed by extending side BC.
To find the measure of angle CAB, we need to consider the relationship between the interior and exterior angles of a triangle. The exterior angle at any vertex of a triangle is equal to the sum of the two remote interior angles.
In this case, we have angle CAB and angle ACB as the two remote interior angles of the exterior angle CBD.
So, the equation becomes:
Angle CAB + Angle ACB = Angle CBD
Substituting the values we have, we get:
(x + 40) + (3x + 10) = 6x
Simplifying, we have:
4x + 50 = 6x
Now, we can solve for x:
6x - 4x = 50
2x = 50
x = 25
Now that we know the value of x, we can substitute it back into the expression for angle CAB:
Angle CAB = x + 40 = 25 + 40 = 65 degrees
Therefore, the measure of angle CAB is 65 degrees.