Question

find the value of unknown angle in the following diagrams​

Answer 1

Answer :

• $\boldsymbol x = y = 90\degree$

Explanation :

In the figure, a triangle with angles $y\degree, 60\degree \: {\sf{and}} \: 30\degree$ is there.

Find the value of unknown angle.

Here,

Using the angle sum property

We can say that,

$\implies y \degree + 30 \degree+ 60\degree = 180 \degree$

Solving for $\boldsymbol y :$

$\implies y \degree + 30 \degree+ 60\degree = 180 \degree$

$\implies y + 90\degree = 180\degree$

$\implies y = 180\degree - 90\degree$

$\implies y = 90\degree$

Now,

Finding the value of $x$ :

We know that,

$\implies x + y = 180\degree \:\:\:\: {\sf{[Linear \: pair ]}}$

We have,

$y = 90\degree$

So,

$\implies x + 90\degree = 180\degree$

$\implies x = 180\degree - 90\degree$

$\implies x = 90 \degree$

Hence,

The value of $\boldsymbol x \:{\sf{and}}\: y \: {\sf{is}} \: 90\degree$

Answer 2

Answer :-

• ${\sf{x~=~y~=90°}}$

Explanation :-

In the figure, a triangle with angles ${\sf{y°}}$ , ${\sf{60°}}$ and ${\sf{30°}}$ is there.

Find the value of unknown angle.

Here,

• Using the angle some property

★ We can say that,

→ ${\sf{y° + 30° + 60° = 180°}}$

Solving for ${\sf{y°}}$:

→ ${\sf{y° + 30° + 60° = 180°}}$

→ ${\sf{y + 90° = 180°}}$

→ ${\sf{y = 180° - 90°}}$

→ ${\sf{y = 90°}}$

Now,

• Finding the value of ${\sf{x}}$ :

★ We know that,

→ ${\sf{x + y = 180°}}$${\sf{\: \: \: \: [Linear \: pair] }}$

We have,

${\sf{y = 90°}}$

So,

→ ${\sf{x + 90° = 180°}}$

→ ${\sf{x = 180° - 90°}}$

→ ${\sf{x = 90°}}$

Hence,

• The value of ${\sf{x}}$ and ${\sf{y}}$ is ${\sf{90°}}$ $\large{\sf\green{✓}}$