Given: Triangle ABC, D belongs to AC, BD=DC, Measure of angle 1 = measure of angle 2, measure of angle BDC = 100 degrees, Find the measure of angle A, B, and C.

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Answer:

m of angle A is 60 degrees, m of angle B is 80 degrees, and m of angle C is 40 degrees

Step-by-step explanation:

Given: BD=DC, this means the triangle BDC is isoceles because of the two equal sides.

Using the base angles Thereom we can tell that m of angle C is equal to m of angle 2.

Given that m of angle BDC is 100 degrees, using sum of angles in triangle we develop the equation

m of angle C= 180-100-angle 2

since angle 2 is equal to angle C we see that they are bothe equal to 40 degrees.

Now for B, we can easily tell it is 80 degrees since we found that angle 2 is 40 degrees and angle 1 is equal to angle 2 40+40=80 degrees

Lastly, for A we can tell it is 60 degrees, the reason is we found angle 1 is 40 degrees and we know that BDA=80 using supplemantary angles to BDC.

Develop the equation A=180-(80+40)=60 degrees

The value of measure of ∠A is, 60° , ∠B is 80° and ∠C is 40°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In Triangle ABC,

D belongs to AC,

BD = DC,

Measure of angle 1 = measure of angle 2,

Measure of angle BDC = 100 degrees.

Here, we have;

⇒ BD = DC

Hence, We get;

⇒ ∠DBC = ∠BCD

(By opposite angle of equal side are equal.)

Now, In ΔBDC;

⇒ ∠BDC + ∠DBC + ∠BCD = 180°

⇒ 100° + 2∠DBC= 180°

⇒ 2 ∠DBC = 180° - 100°

⇒ 2 ∠DBC = 80°

⇒ ∠DBC = 40°

⇒ ∠DBC = ∠BCD = ∠2 = 40°

Hence, ∠ C = 40°

Here, We have to given that;

⇒ ∠1 = ∠2

Hence, ∠1 = ∠2 = 40°

Now, We have by linear pair angle;

⇒ ∠BDC + ∠BDA = 180°

⇒ 100° + ∠BDA = 180°

⇒ ∠BDA = 80°

In ΔABD;

⇒ ∠ABD + ∠BDA + ∠BAD = 180°

⇒ 40° + 80° + ∠BAD = 180°

⇒ ∠BAD = 180° - 120°

⇒ ∠BAD = 60°

⇒ ∠A = 60°

So, ∠ B = ∠1 + ∠2

           = 40° + 40°

           = 80°

Thus, We get;

The value of measure of ∠A is, 60° , ∠B is 80° and ∠C is 40°.

Learn more about the triangle visit;

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