SOLUTION: The perpendicular bisector of side AB of ∆ABC intersects the extension of side AC at D. Find the measure of ∠ABC if m∠CBD = 16� and m∠ACB = 118�.

Question 1102351: The perpendicular bisector of side AB of ∆ABC intersects the extension of side AC at D. Find the measure of ∠ABC if m∠CBD = 16� and m∠ACB = 118�.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let E be the midpoint of side AB, so that DE is the perpendicular bisector of AB.

Then triangle ABD is isosceles; and triangles AED and BED are congruent.

Let F be the point where BC and DE intersect.

Let x be the measure of angle ABC that we are looking for. Then

angle BFE is 90-x [complement of x]
angle BFD is 90+x [supplement of angle BFE]
angle BDF is 74-x [angle sum of triangle BDF, given that angle DBC is 16]

angle ACB is 118 [given]
angle BCD is 62 [supplement of ACB]
angle CFD is 90-x [vertical angle to BFD]
angle CDF is x+28 [angle sum of triangle CFD]

But angles BDF and CDF are corresponding angles in congruent triangles AED and BED, so

The measure of angle ABC is 23 degrees.

There might well be easier ways to get to this result.... The above is what I came up with.

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SOLUTION: The perpendicular bisector of side AB of &#8710;ABC intersects the extension of side AC at D. Find the measure of &#8736;ABC if m&#8736;CBD = 16� and m&#8736;ACB = 118�.

SOLUTION: The perpendicular bisector of side AB of ∆ABC intersects the extension of side AC at D. Find the measure of ∠ABC if m∠CBD = 16� and m∠ACB = 118�.