Question

Please find answer for this​

Answer 1

sum of two opposite sides of interior angle iss equal to the third exterior angle

Then, ANGLE ABC= 180-140

WHERE, Angle ACD = angle BAC + angle ABC

= 180-57 =123 degree

Answer 2

Concept:-

• There are many methods to find <ACD

1. For that first we have to find <ABC and then we have to find < ACB.
2. As we know sum of any two interior angle is equal to opposite exterior angle.

SolUtioN:-

* By first method

➞140° + < ABC = 180° ( Linear pair)

➞ < ABC = 180° - 140°

➞< ABC = 40°

As we know sum of all angles of triangle is 180°

➞ 83° + 40° + <ACB = 180 °

➞ 123 ° + <ACB = 180 °

➞ < ACB = 180 ° - 123 °

➞ <ACB = 57°

➞< ACB + < ACD = 180 ° ( Linear pair)

➞< ACD + 57° = 180 °

➞ < ACD = 180 ° - 57 °

➞ < ACD = 123 °

* By second method

➞140° + < ABC = 180° ( Linear pair)

➞ < ABC = 180° - 140°

➞< ABC = 40°

Now ,

➞< ABC + < CAB = < ACD ( Sum of two interior angle of triangle is equal to opposite exterior angle.

➞ 40° + 83° = < ACD

➞123° = < ACD

___________________

Answer is 123°