MATH SOLVE

4 months ago

Q:
# Which statement about BC←→ is correct?BC←→ is a tangent line because △ABC is a right triangle.BC←→ is a tangent line because the sum of the angles in △ABC is 180º.BC←→ is not a tangent line because m∠ABC≠90°.BC←→ is a tangent line because m∠ABC is acute.

Accepted Solution

A:

Hello!

So a tangent line is perpendicular to the radius, which means it creates a 90 degree angle with the radius of the circle. The sum of the interior angles of any triangle is 180 degrees. To determine if line BC is a tangent line, we have to determine if angle ABC is 90 degrees. Well we know the degrees of the other two angles of the triangle, so let's set up an equation:

180 = 48 + 47 + x

180 = 95 + x

85 = x

Since angle ABC must be 85 degrees (not 90), line BC is not a tangent line.

Answer:

BC←→ is not a tangent line because m∠ABC ≠ 90°.

So a tangent line is perpendicular to the radius, which means it creates a 90 degree angle with the radius of the circle. The sum of the interior angles of any triangle is 180 degrees. To determine if line BC is a tangent line, we have to determine if angle ABC is 90 degrees. Well we know the degrees of the other two angles of the triangle, so let's set up an equation:

180 = 48 + 47 + x

180 = 95 + x

85 = x

Since angle ABC must be 85 degrees (not 90), line BC is not a tangent line.

Answer:

BC←→ is not a tangent line because m∠ABC ≠ 90°.