Q:

please help me with a correct answer

Accepted Solution

A:
Hello!

First, let's find the measure of ∠BCA. We are given that line AD is tangent to circle B. We can also conclude, based on the image above, that line BC is the radius of circle B. Because tangent line AD and radius BC meet at point B. we can conclude that ∠BCA is a right angle.

Right angles have a measure of 90 degrees. We are given that ∠ABC is equal to 40 degrees. Using these two measures, we can calculate the value of ∠BAC. We know that the sum of the angles of any given triangle is equal to 180 degrees. This can be expressed using the following formula:

(angle 1) + (angle 2) + (angle 3) = 180

Insert all known values of triangle ABC into the equation above:

90 + 40 + (angle 3) = 180

Combine like terms:

130 + (angle 3) = 180

Subtract 130 from both sides of the equation:

(angle 3) = 50

We have now proven that the third angle (∠BAC) is equal to 50 degrees.

I hope this helps!