Question

Given that in ΔABC side AB = (3x +10)cm, ∠A = 2x +15° and in ΔPQR side QR = (5y + 15)cm, ∠R = 5x - 60°. Also ΔBAC = ΔQRP by SAS criterion of congruence.
Calculate and select the correct values of x and y

Answer 1

Given : ΔABC side AB = (3x +10)cm, ∠A = 2x +15°  

ΔPQR side QR = (5y + 15)cm, ∠R = 5x - 60°.  

ΔBAC = ΔQRP  by SAS criterion of congruence.

To Find : values of x and y.

Solution:

ΔBAC ≅ ΔQRP by SAS

=>AB = QR

and  ∠A = ∠R

AB = QR

AB = 3x +10

QR = 5y + 15

=> 3x + 10  = 5y + 15

=> 3x  = 5y  + 5

∠A = ∠R

∠A = 2x +15°

, ∠R = 5x - 60°.

=>  2x +15°  = 5x - 60°.

=> 3x = 75°

=> x = 25

3x  = 5y  + 5

=> 3(25) = 5y  + 5

=> 5y = 70

=> y = 14

x = 25

y = 14

Learn More:

in triangle abc angle B equal to angle C show that triangle ABC ...

brainly.in/question/15028174

prove that if two angles and one side of a triangle are equal to two ...

brainly.in/question/21741662

Answer 2

Step-by-step explanation:

✰Question ::-

Given that in ΔABC side AB = (3x +10)cm, ∠A = 2x +15° and in ΔPQR side QR = (5y + 15)cm, ∠R = 5x - 60°. Also ΔBAC = ΔQRP by SAS criterion of congruence.

Calculate and select the correct values of x and y.

✰Solution::-

$\sf∆BAC =~ ∆ QRP \: by \: SAS </u></p><p><u>[tex] \sf∆BAC =~ ∆ QRP \: by \: SAS \\ \sf: \implies AB = QR \: and \: \angle A = \angle R$

AB = QR

• AB = 3x + 16
• QR = 5y + 15

$\sf:\implies 3x + 10 = 5y + 15 \\ </p><p> \sf:\implies 3x + 10 = 5y + 15 \\ \sf:\implies 3x = 5y + 15$

$\bull \: \sf\angle A = \angle R </p><p> \\ \bull \sf\angle A = 2x + 15°</p><p> \\ \bull \sf\angle R = 5x - 60°$

$\sf:\implies 2x + 15° = 5x - 60° </p><p> \\ \sf:\implies 3x = 75 </p><p> \\ \sf:\implies x = \frac{\cancel{75}}{ \cancel3} </p><p> \\ \sf:\implies \fbox \green{ x = 25°}$

$\sf:\implies 3x = 5y + 5 </p><p> \\ \sf:\implies 3(25) = 5y + 5</p><p> \\ \sf:\implies 5y = \dfrac{ \cancel5}{ \cancel{70}}</p><p> \\ \sf:\implies y = \frac{\cancel \red{15}}{\cancel \red{5} } \\ \sf:\implies \: \fbox \blue{y = 14}$

x = 25°

y = 14°

.

Hope it helpful..✨️

@Somya2563