Question

Find the value of X and Y. ​

Answer 1

Required Answer :

[Figure 1]

$\boxed{ \begin{array}{cc} \pmb{ x = {30}^{ \circ} } \\ \pmb{ y = {120}^{ \circ} } \end{array}}$

★ Finding value of x :

As we know that,

• Angles sum property of a triangle states that the sum of all the interior angles of a triangle is 180°. So, according to the question,

➝ 2x° + x° + 90° = 180°

It is a right angled triangle. Hence, the measure of third interior angles is 90°.

➝ 3x° + 90° = 180°

➝ 3x° = 180° – 90°

➝ 3x° = 90°

➝ x° = $\sf \dfrac{90^\circ}{3}$

➝ x° = 30°

★ Finding value of y :

As we know that,

• Exterior angle property of a triangle states that the sum of two interior opposite angles is equal to the measure of exterior angle.

➝ Sum of two interior opposite angles of ∆ = Exterior angle

➝ x° + 90° = y

Substituting the value of x° we found above.

➝ 30° + 90° = y

➝ 120° = y

________________

[Figure 2]

$\boxed{ \begin{array}{cc} \pmb{ x = {50}^{ \circ} } \\ \pmb{ y = {65}^{ \circ} } \end{array}}$

★ Finding value of y :

As we know that,

• Vertically opposite angles are always equal. So, according to the given figure,

➝ 50° and y° are vertically opposite angles.

➝ y° = 50°

★ Finding the value of x :

As we know that,

• Angles sum property of a triangle states that the sum of all the interior angles of a triangle is 180°.

➝ x° + x° + y° = 180°

➝ 2x° + 50° = 180°

➝ 2x° = 180° – 50°

➝ 2x° = 130°

➝ x° = $\sf \dfrac{130^\circ}{2}$

➝ x° = 65°