Explain the concept of interior and exterior angles the figure given

1.	Explain the concept of interior and exterior angles the figure given below. Find x and y.
Answer» The interior angles of a triangle are the three angle elements inside the triangle. The exterior angles are formed by extending the sides of a triangle, and if the side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. Using these definitions, we will obtain the values of x and y. We know that the sum of all angles of a triangle is 180^o. Therefore, for △DBC, we have 30^o + 50^o + ∠DBC = 180^o ∠DBC = 100^o From the figure we can say that x + ∠DBC = 180^o is a Linear pair x = 80^o From the exterior angle property we have y = 30^o + 80^o = 110^o

Explain the concept of interior and exterior angles the figure given below. Find x and y.

Answer»

The interior angles of a triangle are the three angle elements inside the triangle.

The exterior angles are formed by extending the sides of a triangle, and if the side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

Using these definitions, we will obtain the values of x and y.

We know that the sum of all angles of a triangle is 180^o.

Therefore, for △DBC, we have

30^o + 50^o + ∠DBC = 180^o

∠DBC = 100^o

From the figure we can say that

x + ∠DBC = 180^o is a Linear pair

x = 80^o

From the exterior angle property we have

y = 30^o + 80^o = 110^o

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