Question

In triangle ABC, the perpendicular bisector of side AB intersects the extension of side AC at point D. If ∠CBD = 16° and ∠ACB = 118°, find the measure of ∠ABC. A. 16 degrees B. 44 degrees C. 62 degrees D. 74 degrees

Answer 1

Answer:A

Explanation:

To find the measure of angle ABC in triangle ABC, we can use the properties of perpendicular bisectors.

Since the perpendicular bisector of side AB intersects the extension of side AC at point D, we know that AD = DB. Therefore, triangle ABD is an isosceles triangle.

In an isosceles triangle, the angles opposite the equal sides are also equal. So, we have:

∠ABD = ∠ADB

Since ∠CBD = 16° and ∠ACB = 118°, we can find ∠ADB as follows:

∠ADB = 180° - ∠CBD - ∠ACB

= 180° - 16° - 118°

= 46°

Since ∠ABD = ∠ADB, we have:

∠ABD = 46°

Now, we can find ∠ABC:

∠ABC = 180° - ∠ABD - ∠ACB

= 180° - 46° - 118°

= 16°

Therefore, the measure of ∠ABC is 16 degrees. So, the correct answer is A. 16 degrees.