Question

in the given figure below x id five times y. find the value of x, y, z​

Answer 1

Answer:

➪ $x$ = 100°

➪ $y$ = 20°

➪ $z$ = 120°

Step-by-step explanation:

In the triangle ABC :

• ∠A = $x \degree$
• ∠B = $y \degree$
• ∠C = $60 \degree$

Step 1 :

Here, ∠A = $x \degree$ is five times ∠B = $y \degree$

So we can say that,

∠A = $x \degree = 5y \degree$

Using the angle sum property of △ :

→ ∠A + ∠B + ∠C

We have,

• ∠A = $5y \degree$
• ∠B = $y \degree$
• ∠C = $60 \degree$

So,

$\implies 5y \degree + y \degree + 60 \degree = 180 \degree$

$\implies 6y \degree + 60 \degree = 180\degree$

$\implies 6y \degree = 180\degree - 60\degree$

$\implies 6y = 120\degree$

$\implies y \degree = \dfrac{120}{6}$

$\implies y \degree = 20 \degree$

Therefore, the value of $y$ is 20°

And also, $x = 5y = 5(20) = 100 \degree$

Step 2 :

Finding the value of $z$ :

We know that,

∠ACD + ∠ACB = 180°

• Linear pair.

We have,

• ∠ACD = $z$
• ∠ACB = $60 \degree$

So,

$\implies z$ + 60° = 180°

$\implies z$ = 180° - 60°

$\implies z$ = 120°

Therefore, the value of $z$ = 120°

Note behind :

• Linear pair : Two Adjacent angles in a line forms 180° is known as the linear pair.
• Angle sum property of a △ : Any traingle's all angles sums to 180° is called as Angle sum property of a triangle.

Answer 2

$\huge \mathfrak{ \color{pink}{An}} \mathfrak{ \color{plum}{sw}} \mathfrak{ \color{violet}{er}}$

$\sf➪ x = 100° \\ \sf➪ y = 20 ° \\ \sf➪ z = 120°$

$\large \mathfrak{ \color{deepskyblue}{Step}}{\mathfrak{\blue{-by-}}} {\mathfrak{ \color{royalblue}{step}}} {\mathfrak{ \color{blue}{ \: Explanation}}}$

In the triangle ABC :

• ∠A = x°
• ∠B = y°
• ∠C = 60°

$\large {\textsf{ \textbf{ \color{mediumaquamarine}{Step 1 :}}}}$

Here, 

∠A = x° is five times ∠B = y°

So we can say that,

∠A = x° = 5y°

Using the angle sum property of △ :

→ ∠A + ∠B + ∠C

We have,

• ∠ A = 5y°
• ∠ B = y°
• ∠ C = 60°

So,

$\implies\sf{5y° + y° + 60° = 180°}$

$\implies\sf{6y° + 60° = 180°}$

$\implies\sf{6y° = 180° − 60°}$

$\implies\sf{6y = 120°}$

$\implies\sf {y°= \dfrac{120}{6}}$

$\implies\sf {y° = 20 \degree}$

Therefore, the value of y is 20°

And also, x = 5y = 5(20) = 100°

$\large {\textsf{ \textbf{ \color{mediumaquamarine}{Step 2 :}}}}$

Finding the value of z :

We know that,

∠ACD + ∠ACB = 180° Linear pair.

We have,

• ∠ACD = zz
• ∠ACB = 60°

So,

$\implies\sf{z + 60° = 180°}$

$\implies\sf{z = 180° - 60°}$

$\implies\sf{z = 120°}$

Therefore, the value of z = 120°