Question

1) In the figure fend the values of x and y​

Answer 1

Answer:

x=20.5 ,y=16

Step-by-step explanation:

2(x-5)=51

2x-10=51

   2x =51-10

     x = 41/2

      x=20.5

3(y+4)=60

3y+12=60

   3y  =60-12

      y = 48/3

      y=16

Answer 2

Given :

$Side \: PQ ≅ \: Side \: PS \\ Side RS ≅ Side RQ \\ \: \angle PQS = 2 (x -5) \degree \\ \angle PSQ = 60 \degree \: \: \: \: \: \: \: \: \: \: \: \: \\ \angle RSQ = 3(y+4) \degree \\ \angle RQS = 51\degree \: \: \: \: \: \: \: \: \: \:$

To find :

$• Value \: of \: x \: and \: y$

Solution :

$In \: ∆PQS, \\ Side \: PQ ≅ Side \: PS - ( Given )$

Isosceles triangle theorem : If two sides of a triangle are congruent then the angles opposite to them are congruent

$\angle PQS = \angle \: PSQ \\ 2(x - 5) \degree = 60 \degree \\ x - 5 = \frac{60}{2} \\ x - 5 = 30 \degree \\ x = 30 + 5 \\ \boxed{ \blue{ x = 35 \degree}}$

$In ∆ RQS , \\ Side \: RS ≅ Side \: RQ - ( Given ) \\ \angle RSQ \: = \angle RQS \\ - [ Isosceles \: triangle \: theorem ] \\ 3(y + 4) \degree \: = 51 \degree \\ y + 4 = \frac{51}{3 } \\ y + 4 = 17 \degree \\ y = 17 - 4 \\ \boxed{ \blue {y = 13 \degree}}$

Verification :

$1) \: \angle PQS = 2(x-5)° \\ = 2(35 - 5) \degree \\ = 2(30) \degree \\ = 60 \degree \\ \\ 2) \angle \: RSQ = 3(y+4)° \\ = 3(13 + 4) \degree \\ = 3(17) \degree \\ = 51 \degree$