Question

Triangle angle sum theorem and exterior angle theorem

Answer 1

the angle sum of triangle is 180 degrees. it can be explained because all the angle sum is just the number of sides - 2 and multiply them by 180.
and the exterior angle sum of any sides of polygon, including triangle is always 360 degrees

Answer 2

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