Question

In triangle ABC, side BC is extended through C to D. If the measure of angle BCD is 30° and the measure of angle ACD is 110°, what is the longest side of triangle ABC?

Answer 1

By calculating the measures of the angles within triangle ABC, we can determine that the longest side of the triangle is opposite the largest angle.

Step-by-step explanation:

The question pertains to angles in a triangle and finding the longest side. In triangle ABC, with BC extended through C to D, angle BCD is given as 30° and angle ACD as 110°.

From the geometry, one can deduce that angle ACB is 40° (since 110° + 30° + angle ACB = 180° for a straight line at point C).

Furthermore, in triangle ABC, the sum of the angles will be 180°.

Therefore, if we subtract angles ABC and ACB from 180°, we can find angle BAC. Using the knowledge that the longest side of a triangle is opposite the largest angle,

we can then determine which side of triangle ABC is the longest based on the angle measures.