Question

7. Find the value of x and y in the below figure.
y
30°
X
600​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given a triangle and some measurements. We have to find the value of unknown angles.

Here, we have to use two properties :

• Angle sum property of ∆ :

$\longmapsto$ Sum of interior angles of ∆= 180°

• Vertically opposite angles of two intersecting lines are always equal.

_______________

$\Large {\underline { \sf {Explication \: of \: Steps :}}}$

$\underline{\small \sf {\maltese \; \; \; Finding \: value\: of \: x^{\circ} : \; \; \; }}$

As we know that,

>> Vertically opposite angles of two intersecting lines are always equal.

So,

$\implies\boxed{ \sf \red{ x^{\circ} = 60^{\circ} }}$

_______________

$\underline{\small \sf {\maltese \; \; \; Finding \: value\: of \: y^{\circ} : \; \; \; }}$

We know that,

>> Sum of interior angles of ∆ is equivalent to 180°.

So,

$\implies \sf { 30^{\circ} + x^{\circ} + y^{\circ} = 180^{\circ} }$

Substituting value of x° we got above.

$\implies \sf { 30^{\circ} + 60^{\circ} + y^{\circ} = 180^{\circ} }$

$\implies \sf { 90^{\circ} + y^{\circ} = 180^{\circ} }$

$\implies \sf { y^{\circ} = 180^{\circ} - 90^{\circ} }$

$\implies\boxed{ \sf \red{ y^{\circ} = 90^{\circ} }}$

Therefore, value of x° is 60° and value of y° is 90°.

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$\Large {\underline { \sf {A \: Little \: Further !}}}$

More about triangles :

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 $\sf {\dfrac{a+b+c}{2} }$