find the measure of the angle in the triangle?

Question

Triangle ABC is an isosceles triangle with the measure of angle B = the measure of angle C, and the measure of angle A = 20 degrees. Points D and E are located on sides AC and AB, respectively, so the the measure of angle CBD = 50 degrees and the measure of angle BCE = 40 degrees. Determine the measure of the angle BDE.

Answer 1

Angle BDE = 30 degrees

First, since you have an isoceles triangle, with A being 20 degrees, that means that angles B and C will be 80 degrees (20 + 80 + 80 = 180).

CBD is 50 degrees, so CBD is 30.
Similarly:
BCE is 40 degrees, so DCE is also 40 degrees.

Your two lines (BD and CE) cross at a point, let's call that F.
If you check the measurements of the triangles around it, you'll see that the four angles around F are all 90 degrees.

Triangle CBF = 40-50-90
Triangle CDF = 40-50-90
Triangle BEF = 30-60-90

Since CBF and CDF are congruent triangles, it follows that BEF and DEF must be congruent triangles.

Therefore BDE must be 30 degrees.

Answer 2

Addition of all angles of a given triangle should equal 180 degrees. Example: If two anges are 20 degrees, then the last angel is 180-20-20=140 degrees.
Draw yourself a picture.
The intersection of the two lines is right angled. Everything is similar.
If you are still having trouble e-mail me.

Answer 3

Therefore EC _|_ BD (50° + 40° + 90° = 180°)
Also Therefore Δ BDC is isosceles and since EC _|_ BD, EC bisects BD
So BEDC is a kite and EB = ED (properties of a kite)
So Δ BDE is isosceles.
Now Therefore

Answer 4

BDE = 40