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°.

°

Step-by-step explanation:

Let the measure of

Let the perpendicular bisector of AB meet AB at E as shown in the figure below.

Given:

°, °

Consider the triangles Δ AED and Δ BED

AE ≅ BE  (Perpendicular bisector bisects the side equally)

° (Perpendicular bisector bisects the side at right angles)

ED ≅ ED ( Reflexive property)

Therefore, Δ AED ≅ Δ BED by SAS postulate.

Now, by CPCTE,

Now, consider the triangle Δ ABC,

The sum of all its interior angles is equal to 180°. Therefore,

Therefore, the measure of °.

a

step-by-step explanation: