Question

The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees

Answer 1

23°

Explanation:

Let the interior angles of ΔABC be referenced by A, B, and C. The definition of point D means that ΔDAB is an isosceles triangle, so we have the relations ...

A + B + 118 = 180 . . . . interior angles of ΔABC

A = B +16 . . . . . . . . . . base angles of ΔDAB

Using the expression for A in the second equation to substitute into the first equation, we get ...

(B+16) +B +118 = 180

2B + 134 = 180 . . . . . collect terms

2B = 46 . . . . . . . . . . . subtract 134

B = 23 . . . . . . . . . . . . divide by 2

m∠ABC = 23°