Question

Find the value of x and y in the figure below

Answer 1

• x = -12
• y = 9

Explanation:

Now we have to,

→ Find the required value of x and y.

We know that,

→ Vertically opposite angles are equal.

Forming the equations,

→ 7y + 60° = 11y + 24°

→ 5x + 117° = 3x + 93°

Let's find required value of y,

→ 7y + 60° = 11y + 24°

→ 7y - 11y = 24° - 60°

→ -4y = -36

→ 4y = 36

→ y = 36/4

→ [ y = 9 ]

Then the value of x will be,

→ 5x + 117° = 3x + 93°

→ 5x - 3x = 93° - 117°

→ 2x = -24

→ x = -24/2

→ [ x = -12 ]

Hence, the value of x is -12.

Answer 2

x = - 12 , y = 9

Explanation:

(5x + 117) and (3x + 93) are vertically opposite angles and are congruent, so

5x + 117 = 3x + 93 ( subtract 3x from both sides )

2x + 117 = 93 ( subtract 117 from both sides )

2x = - 24 ( divide both sides by 2 )

x = - 12

similarly

(11y + 24) and (7y + 60) are vertically opposite angles and are congruent, so

11y + 24 = 7y + 60 ( subtract 7y from both sides )

4y + 24 = 60 ( subtract 24 from both sides )

4y = 36 ( divide both sides by 4 )

y = 9