Find Angle Beta

[nycmathguy]

 

[MathLover1]

triangle ABC is isoscales => AC=BC

< A=2theta
AB=AD
find angle beta

since given AB=AD triangle ABD is isoscales

then < B= <BDA = < A=2theta
since third angle in triangle ABD is <DAB=theta
then the sum of all angles in ABD is:
theta+2theta+2theta=180
5theta=180.........eq.1

now observe triangle ADC

<BDA and <ADC form strait angle, so their sum is 180
since <BDA =2theta and from eq.1 5theta=180 , then <ADC=3theta
and since <CAD=theta

the sum of all angles in triangle ADC is

beta+<CAD+<ADC=180
beta+theta+3theta=5theta
beta+4theta=5theta
beta=5theta-4theta
beta=theta

 

[nycmathguy]

triangle ABC is isoscales => AC=BC

< A=2theta
AB=AD
find angle beta

since given AB=AD triangle ABD is isoscales

then < B= <BDA = < A=2theta
since third angle in triangle ABD is <DAB=theta
then the sum of all angles in ABD is:
theta+2theta+2theta=180
5theta=180.........eq.1

now observe triangle ADC

<BDA and <ADC form strait angle, so their sum is 180
since <BDA =2theta and from eq.1 5theta=180 , then <ADC=3theta
and since <CAD=theta

the sum of all angles in triangle ADC is

beta+<CAD+<ADC=180
beta+theta+3theta=5theta
beta+4theta=5theta
beta=5theta-4theta
beta=theta

What can I say? You are the best.