Question

In △abc, the perpendicular bisector of side ab intersects the extension of side ac at point d. find the measure of ∠abc if m∠cbd=16° and m∠acb=118°.

Answer 1

The measure of ∠ABC in triangle ABC is 46°, calculated using the sum of angles in a triangle and the given measures of ∠CBD and ∠ACB.

Step-by-step explanation:

To find the measure of ∠ABC in triangle ABC, we can utilize the properties of the triangle and the given angles. Since the perpendicular bisector of side AB intersects the extension of side AC at point D, and given that m∠CBD=16° and m∠ACB=118°, we can proceed to find the unknown angle.

First, we acknowledge that the sum of the angles within any triangle is 180°. Thus, we can set up an equation to find the measure of ∠ABC:

1. m∠ABC + m∠ACB + m∠CBA = 180°
2. m∠ABC + 118° + m∠CBD = 180°
3. m∠ABC + 118° + 16° = 180°
4. m∠ABC = 180° - 118° - 16°
5. m∠ABC = 46°

Therefore, the measure of ∠ABC is 46°.

Answer 2

In triangle ABC, the perpendicular bisector of side AB intersects the extension of side AC at point D. Angle ABC can be found by subtracting the measures of angle CBD and angle ADB from 180°.

Step-by-step explanation:

In triangle ABC, the perpendicular bisector of side AB intersects the extension of side AC at point D. We are given that angle CBD is 16° and angle ACB is 118°. To find angle ABC, we can use the fact that a perpendicular bisector divides a line segment into two congruent halves. This means angle ADB is also 16°, since angle CBD and angle ADB are vertical angles. Since angle ADB and angle ACB form a straight line, their measures add up to 180°. Therefore, angle ABC = 180° - angle CBD - angle ADB = 180° - 16° - 16° = 148°.