Question

In the given figure, side BC of Triangle ABC has been produced to a point D. If ZA
= 3yº, Angle B = x°, Angle C=5yº and Angle CBD = 7yº. Then, the value of x is
(a) 60
(b) 50
(c) 45
(d) 35​

Answer 1

Answer:

<CBD is a misprint it should be <DCA

<BCA+<DCA = 180° (linear pair)

5y+7y = 180

12y = 180

y = 15

<BCA = 15×5 = 75°

<DCA = 15×7 = 105°

<BAC = 15×3 = 45°

now from here you can find it in two ways...

1) exterior angle property.

2) angle sum property.

1) <DCA = <BAC+<CBA (exterior angle property)

=> 105° = 45°+x

=> x = 60°

or by 2nd method....

2) <BAC+<ACB+<CBA = 180° (Angle sum property of triangle)

45°+75°+x = 180°

120°+x = 180°

x = 60°

Hope it will help you!

Answer 2

Given  : side BC of Triangle ABC has been produced to a point D.

∠A= 3yº, ∠B = x°, ∠C=5yº and ∠ACD = 7yº.  

To Find : the value of x  

(a) 60

(b) 50

(c) 45

(d) 35​

Solution:

side BC of Triangle ABC has been produced to a point D.

Hence BCD is a straight line

=> ∠C + ∠ACD = 180°  linear pair

=> 5y° + 7y° = 180°

=> 12y° = 180°

=> y = 15

Sum of angles of a triangle is 180°

x° + 3y° + 5y° = 180°

=> x° + 8y° = 180°

=> x° + 8(15)° = 180°

=> x° + 120° = 180°

=> x° = 60°

=> x = 60

Hence correct option is  a) 60

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