Question

Find value of x and y in given figure ​

Answer 1

Required Answer:

(i)

→ y = 80°

(Since, the vertically opposite angles are equal.)

As per the property of triangles ,

• Angle sum property of the ∆ implies that the sum of the interior angles of a triangle is equivalent to 180°. So,

→ 50° + y + x = 180°

Substitute the value of y we got above,

→ 50° + 80° + x = 180°

→ 130° + x = 180°

→ x = 180° - 130°

→ x = 50°

Therefore, value of x is 50° and value of y is 80°.

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(ii)

As per the property of triangles ,

• Angle sum property of the ∆ implies that the sum of the interior angles of a triangle is equivalent to 180°. So,

→ 50° + 60° + y = 180°

→ 110° + y = 180°

→ y = 180° - 110°

→ y = 70°

Now, we know that :

• Sum of all the angles that lie on the straight line is 180°. So by linear pair,

→ x + y = 180°

Substitute the value of y we got above,

→ x + 70° = 180°

→ x = 180° - 70°

→ x = 110°

Therefore, value of x is 110° and value of y is 70°.

A little further...!

Important properties of triangle :

★ Angle sum property of a triangle :

• Sum of interior angles of a triangle = 180°

★ Exterior angle property of a triangle :

• Sum of two interior opposite angles = Exterior angle

★ Perimeter of triangle :

• Sum of all sides

★ Area of triangle :

• $\sf { \dfrac{1}{2} \times Base \times Height }$

★ Area of an equilateral triangle:

• $\sf { \dfrac{\sqrt{3}}{4} \times {Side}^{2} }$

★ Area of a triangle when its sides are given :

• $\sf { \sqrt{s[ (s-a)(s-b)(s-c) ]} }$

Where,

• S= Semi-perimeter or $\sf {\dfrac{a+b+c}{2} }$