Question

In a quadrilateral ABCD, A+ B = 182 and B +C = 150°. If D = 100°, then the sum of the least and greatest angles of ABCD is pls answer in simple way I will give 15 points ​

Answer 1

Answer:

182

A+B+C+D=360

C+D=360-182=178

C=178-100=78

B=150-78=72

A=360-250=110

SUM OF A AND B= 110+72=182

Answer 2

Answer: The sum of the least and the greatest angle of quadrilateral ABCD is 182°

Step-by-step explanation:

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are ∠A, ∠B, ∠C, and ∠D.

In a quadrilateral ABCD it is given in the question that
∠A+∠B = 182°
∠B +∠C = 150°
∠D = 100°

Sum of angles of a quadrilateral is 360°

∠A+∠B+∠C+∠D = 360°

⇒(∠A+∠B)+∠C+∠D = 360°
⇒ 182° + ∠C + 100° = 360°
⇒ ∠C + 282° = 360°
⇒ ∠C = 78°
Putting ∠C = 78° in above we get:
⇒ ∠B +∠C = 150°
⇒ ∠B = 150° - 78° = 72°

⇒ ∠B = 72°
Putting ∠B = 72° in above we get
⇒ ∠A+∠B = 182°

⇒ ∠A + 72° = 182°
⇒ ∠A = 182°- 72°= 110°

⇒ ∠A = 110°

least angle is ∠B which is 72° and the greatest angle is ∠A which is 110°

Thus, its sum = 72° + 110° = 182°

Hence, the sum of the least and the greatest angle of quadrilateral ABCD is 182°

To know more, click here:
https://brainly.in/question/22237063
https://brainly.in/question/14381264
#SPJ2