Question

In the figure M angle 11=62 and M angle 14=38 find the measure of each angle. tell which postulate or theorems you used

Answer 1

We are given

angle(11)=62

angle(14)=38

Calculation of angle(1):

we know that

angle(1) and angle(9) are corresponding angles

so,

angle(1)=angle(9)

and angle(9) and angle(14) are vertically opposite angles

so, angle(9)=angle(14)=38

so, angle(1)=angle(9)=angle(14)=38

angle(1)=38

angle(9)=38

Calculation of angle(3):

we know that angle(3) and angle(8) are corresponding angles

so, angle(3)=angle(8)

and angle(8) and angle(11) are vertically opposite angles

so,

angle(3)=angle(8)=angle(11)=62

so,

angle(3)=62

angle(8)=62

Calculation of angle(2):

we know that

angle(1) , angle(2) and angle(3) form supplementary angles

so,

angle(1) + angle(2)+angle(3)=180

we can plug values

38 + angle(2)+62=180

angle(2)=80

Calculation of angle(4):

Since, angle(4) and angle(3) are vertically opposite angles

so,

angle(4)=angle(3)=62

so,

angle(4)=62

Calculation of angle(5):

Since, angle(5) and angle(2) are vertically opposite angles

so,

angle(5)=angle(2)=80

so,

angle(5)=80

Calculation of angle(6):

Since, angle(6) and angle(1) are vertically opposite angles

so,

angle(6)=angle(1)=38

so,

angle(6)=38

Calculation of angle(7):

Since, angle(7) and angle(8) are supplementary angles

so, angle(7)+angle(8)=180

angle(8)=62

angle(7)+62=180

angle(7)=118

Calculation of angle(10):

Since, angle(9) and angle(10) are supplementary angles

so, angle(9)+angle(10)=180

angle(9)=38

angle(10)+38=180

angle(10)=142

Calculation of angle(12):

Since, angle(7) and angle(12) are vertically opposite angles

so,

angle(7)=angle(12)=118

angle(12)=118

Calculation of angle(13):

Since, angle(10) and angle(13) are vertically opposite angles

so,

angle(10)=angle(13)=142

angle(13)=142

So, our angles are

angle(1)=38

angle(2)=80

angle(3)=62

angle(4)=62

angle(5)=80

angle(6)=38

angle(7)=118

angle(8)=62

angle(9)=38

angle(10)=142

angle(11)=62

angle(12)=118

angle(13)=142

angle(14)=38..............Answer

Answer 2

from the given figure two lines are parallel to each other. If ∠11=62 then ∠12 =(180- 62)=118,∠8=62 (vertically opposite angles are parallel) and ∠4=62 corresponding angles are equal )If ∠8=62 then ∠3=62 (corresponding angles in a parallel lines are equal)  If ∠14=38 then∠13=(180-38)=142 , ∠6=38 (corresponding angles) and ∠9=38 (vertically opposite angles). If ∠6=38 then∠1=38 (vertically opposite angles) If ∠1=38 and ∠3=62 then ∠2=180-(38+62)=80 and if ∠2=80 then ∠5=80 (vertically opposite angles)