In the figure given alongside, find the values of x and y.

1.	In the figure given alongside, find the values of x and y.
Answer» In the given figure, side BC of ΔABC is produced to D. Consider the ΔABC, We know that the exterior angle of a triangle is equal to the sum of its interior opposite angles. ∴ ∠ABC + ∠BAC = ∠ACD = x^o + 32^o = 65^o = x = 65^o – 32^o = x = 33^o Also, we know that the sum of all the angles of a triangles is 180^o. ∴ A + B + C = 180^o = 32^o + x^o + y^o = 180^o = 32^o + 33^o + y^o = 180^o = y + 65^o = 180^o = y = 180^o – 65^o = y = 115^o Hence, the value of x is 33^o and value of y is 115^o.

Answer»

In the given figure, side BC of ΔABC is produced to D.

Consider the ΔABC,

We know that the exterior angle of a triangle is equal to the sum of its interior opposite angles.

∴ ∠ABC + ∠BAC = ∠ACD

= x^o + 32^o = 65^o

= x = 65^o – 32^o

= x = 33^o

Also, we know that the sum of all the angles of a triangles is 180^o.

∴ A + B + C = 180^o

= 32^o + x^o + y^o = 180^o

= 32^o + 33^o + y^o = 180^o

= y + 65^o = 180^o

= y = 180^o – 65^o

= y = 115^o

Hence, the value of x is 33^o and value of y is 115^o.

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