Question

Please Solve This Q1 Two complementary angles are (y + 4)° and (2y – 7)°, find the value of y
Q2 In the given figure, find the value of 'x'

Answer 1

✬ Y = 31° ✬

✬ x = 50° ✬

Step-by-step explanation:

Given:

• Meaure of two complementary angles are (y + 4)° and (2y – 7)°.

To Find:

• What is the value of y ?

Solution: If the sum of two angles is of 90°. Then it is said to be complementary angle. Therefore

➟ (y + 4)° + (2y – 7)° = 90°

$\implies{\rm }$ y + 4 + 2y – 7 = 90

$\implies{\rm }$ 3y – 3 = 90

$\implies{\rm }$ 3y = 90 + 3

$\implies{\rm }$ 3y = 93

$\implies{\rm }$ y = 93/3

$\implies{\rm }$ y = 31°

Hence, the value of y is 31°.

____________________

Given:

• Values of angle are (x + 3)° , (x + 20)° and (x + 7)°.

To Find:

• What is the value of x ?

Solution: Here all these angles are in Linear pair so their sum will be of 180°.

➟ ∠DBE + ∠DBC + ∠CBF = 180°

➟ (x + 3)° + (x + 20)° + (x + 7)° = 180

$\implies{\rm }$ x + 3 + x + 20 + x + 7 = 180

$\implies{\rm }$ 3x + 30 = 180

$\implies{\rm }$ 3x = 180 – 30

$\implies{\rm }$ 3x = 150

$\implies{\rm }$ x = 150/3

$\implies{\rm }$ x = 50°

Hence, the value of x is 50°.

Answer 2

Given :

• Complementary angles are (y + 4)° and (2y - 7)°

To find :

• The value of y.

According to the question,

• Complementary angle is 90°

➨ (y + 4)° + (2y - 7)° = 90°

➨ y + 4 + 2y - 7 = 90°

➨ 3y - 3 = 90°

➨ 3y = 90° + 3

➨ 3y = 93°

➨ y = 93° ÷ 3

.°. y = 31°

_________________....

Given :

•  ∠ EOB = (x + 3)°
•  ∠ DBC = (x + 20)°
•  ∠ CBF = (x + 7)°

To find :

• Value of x.

According to the question,

➨  ∠ EOB + ∠ DBC + ∠ CBF = 180°

➨ (x + 3)° + (x + 20)° + (x + 7) = 180°

➨ x + 3 + x + 20 + x + 7 = 180°

➨ 3x + 30° = 180°

➨ 3x = 180° - 30°

➨ 3x = 150°

➨ x = 150° ÷ 3

.°. x = 50°

____________...

• Value of y = 31°
• Value of x = 50°