Equilateral triangle ABC and isosceles triangle DBC share side BC. If angle BDC= 34 and BD=BC, what is the measure of angle ABD?
I don't know how to solve this questions, can someone guide me through?
Start by drawing a diagram.
If BC=BD, then
∠BDC=∠BCD=34° (angles opposite equal sides.
Hence ∠CBD=180-(34+34)=112°
∠ABD=∠ABC+∠CBD=?
Recall that ΔABC is equilateral.
All angles in the equilateral triangle are 60°
In the isosceles triangle the two base angles are
73 ° each ......... ( (180-34)/2 )
so angle ABD = 60+73 or 133°
Go with MathMate, I misread the question
To solve this question, we can use the properties of isosceles triangles and the fact that angles in a triangle add up to 180 degrees.
First, let's label the angles in triangle ABC. Since it is an equilateral triangle, all of its angles are equal, so angle BAC = angle ABC = angle BCA.
Since angle DBC = 34 degrees, and BD=BC, it means that triangle BDC is an isosceles triangle. In an isosceles triangle, the base angles (the ones opposite the congruent sides) are equal.
Therefore, angle BCD = angle BDC = 34 degrees.
Since the angles in triangle BCD add up to 180 degrees, we can find the measure of angle CBD:
Angle CBD + angle BCD + angle BDC = 180 degrees
Let's substitute the known values:
Angle CBD + 34 degrees + 34 degrees = 180 degrees
Combine like terms:
Angle CBD + 68 degrees = 180 degrees
Now, isolate angle CBD:
Angle CBD = 180 degrees - 68 degrees
Angle CBD = 112 degrees
Since triangle ABC is equilateral, all its angles are equal, including angle BAC. Therefore, angle ABD is equal to:
Angle ABD = angle BAC = angle ABC = angle BCA
Since the sum of the angles in triangle ABC is 180 degrees, we can find the measure of angle ABD:
Angle ABD + angle BAC + angle ABC = 180 degrees
Let's substitute the known values:
Angle ABD + angle ABD + angle ABD = 180 degrees
Combine like terms:
3 * Angle ABD = 180 degrees
Now, isolate Angle ABD:
Angle ABD = 180 degrees / 3
Angle ABD = 60 degrees
Therefore, the measure of angle ABD is 60 degrees.