Answer:
5.\(m\angle 1=47^{\circ}\)
\(m\angle 2=137^{\circ}\)
\(m\angle 3=31^{\circ}\)
7.\(m\angle 1=87^{\circ}\)
\(m\angle 2=45^{\circ}\)
\(m\angle 3=45^{\circ}\)
\(m\angle 4=52^{\circ}\)
Step-by-step explanation:
5.\(\angle 1+43^{\circ}+90^{\circ}=180^{\circ}\)
By triangle angle sum theorem
\(\angle +133^{\circ}=180^{\circ}\)
Addition property of integers
\(\angle 1=180-133=47^{\circ}\)
By using subtraction property of equality
\(m\angle 1=47^{\circ}\)
\(m\angle 2=90+47=137^{\circ}\)
By using exterior angle theorem
\(90+47+12+m\angle 3=180^{\circ}\)
By using triangle angle sum theorem
\(149+m\angle 3=180\)
Addition property of integers
\(m\angle 3=180-149=31^{\circ}\)
Using subtraction property of equality
\(m\angle 3=31^{\circ}\)
7.We are given that
\(m\angle ACD=90^{\circ}\)
BC bisects angle ACD
\(m\angle 2=m\angle 3\)
Therefore, \(m\angle 2=\frac{90}{2}=45^{\circ}\)
\(m\angle 2=m\angle 3=45^{\circ}\)
\(m\angle 1+m\angle 2+48=180^{\circ}\)
By using triangle angle sum theorem
Substitute the value
\(45+m\angle 1+48=180\)
\(m\angle 1+93=180\)
By addition property of integers
\(m\angle 1=180-93=87^{\circ}\)
By using subtraction property of equality
\(m\angle 3+m\angle 4+83=180^{\circ}\)
By using triangle angle sum property
Substitute the values
\(45+m\angle 4+83=180\)
\(128+m\angle 4=180\)
Using addition property of integers
\(m\angle 4=180-128=52^{\circ}\)
Using subtraction property of equality
