Question

find the value of x,y and z
plz answer
I will make brainliest ​

Answer 1

Here,

∠ PQR + 80° = 180° { By Exterior ∠ property}

★ The sum of interior and exterior angle is to be equal to 180 °

From this,

∠ PQR = 180° - 80 °

∠ PQR = 100°

∠ PQR = x = 100 ° { By opposite Angle of // gm }

Opposite Angle of // gm are equal.

In ∆ PSR , Applying Angle Sum property of Triangle.

According to this, the sum of all the angles is equal to 180°

Then,

∠ 60 ° + 100 ° + ∠ PRS = 180 °

∠ 160 ° + ∠ PRS = 180 °

∠ PRS = 180 ° - 160 °

∠ PRS = 20 °

Now, ∠ PRS = 20° = z { By Alternate Angle }

Therefore, In ∆ PQR

Using Angle sum property of the triangle.

★ Sum of angles = 180 °

∠ 20 ° + ∠ PRQ + 100° = 180 °

∠ 120 ° + ∠ y = 180 °

∠ y = 180 ° - 120 °

∠ y = 60 °

Therefore,

• → ∠ x = 100 °

• → ∠ z = 20 °

• → ∠ y = 60 °

__________________________

For more information regarding angle relations , refer to this questions too :

• Find the value of x. if l || m

→ https://brainly.in/question/36278693

$\Large{\underline{\bf{Solution:-}}}$

Here we go!

☆ Internal opposite angles are equal

☆ External opposite angles are equal

☆ Adjacent angles add up to 180°

☆ Co-interior angles add up to 180°

☆ Vertically Opposite Angles are equal....

Answer 2

❒ Find the value of x , y & z from the given Parallelogram.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Finding the value of x in the parallelogram.

As , We know that ,

• The sum of Exterior angle and Interior angle is equal to 180⁰ .

Or ,

• $\sf{Interior \: Angle + Exterior\:Angle = 180\degree}$

Or,

⠀⠀⠀⠀⠀$:\implies \sf{\angle PQR + 80\degree = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{\angle PQR = 180\degree - 80\degree }$

⠀⠀⠀⠀⠀$:\implies \sf{\angle PQR = 100\degree}$

As , We know that ,

• Vertically Opposite angle of Parallelogram are always equal .

Then ,

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 100\:degree}}}}\:..[Vertically\:Opposite \:to\:\angle PQR]\bf{\bigstar}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Finding the value of z in the parallelogram.

As We know that ,

• The sum all three angles of Triangle is 180⁰

Or ,

⠀⠀⠀⠀⠀$:\implies \sf{\angle PSR + \angle SPR + \angle PRS = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{100\degree + 60\degree + \angle PRS = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{160\degree + \angle PRS = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{ \angle PRS = 180\degree-160\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{ \angle PRS = 20\degree}$

As We now that ,

• Alternate angles of Parallelogram are always equal.

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  z = 20\:degree}}}}\:..[Alternate \:\:angle ]\bf{\bigstar}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Finding the value of y in Parallelogram.

As We know that ,

• The sum all three angles of Triangle is 180⁰

Or ,

⠀⠀⠀⠀⠀$:\implies \sf{\angle PQR + \angle PRQ + \angle PRQ = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{100\degree + 20\degree + \angle PRQ = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{160\degree + \angle PRQ = 180\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{\angle PRQ = 180\degree-120\degree}$

⠀⠀⠀⠀⠀$:\implies \sf{\angle PRQ = 16\degree}$

Or ,

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  z = 60\degree}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Hence ,

• $\sf{ The\:Value\:of\:x\:is\:\bf{100\degree}}$
• $\sf{ The\:Value\:of\:y\:is\:\bf{20\degree}}$
• $\sf{ The\:Value\:of\:z\:is\:\bf{60\degree}}$

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