Question

One of the angles of a parallelogram is 75 degrees. Find the measures of the remaining angles of the parallelogram

Answer 1

✬ Angles = 105° , 105° , 75° ✬

Step-by-step explanation:

Given:

• One angle of parallelogram is 75°.

To Find:

• Measures of remaining angles of parallelogram ?

Solution: Let GFEX be a parallelogram where

• GF || EX
• GX || FE
• ∠G = 75°

Let other pair of opposite angles be of x°.

As we know that opposite angles of parallelogram are equal to each other therefore,

• ∠G = ∠E = 75°
• ∠F = ∠X = x°

★ Sum of all angles of ||gm = 360° ★

$\implies{\rm }$ ∠G + ∠F + ∠E + ∠X = 360°

$\implies{\rm }$ 75° + x + 75° + x = 360°

$\implies{\rm }$ 2x = 360 – 150

$\implies{\rm }$ x = 210/2

$\implies{\rm }$ x = 105°

Hence, other angles are

➙ ∠F is x = 105°

➙ ∠X is x = 105°

_____________

★ Verification ★

➟ 105° + 105° + 75° + 75° = 360°

➟ 210° + 150° = 360°

➟ 360° = 360°

$\large\boxed{\texttt{Verified}}$

Answer 2

$\large\mathcal\green{\underbrace{QUESTION:-}}$

One of the angles of a parallelogram is 75 degrees. Find the measures of the remaining angles of the parallelogram.

$\large\mathcal\red{\underbrace{SOLUTION:-}}$

It is Given that,

One Angle Is 75°.

We know that,

Opposite Angles Of Parallelogram are equal.

So, Another Angle = 75°

Rest Two Angles Are Equal.

So, Let the other angles be x.

Now, Formula Applied :-

Sum Of All Angles Of ||gm = 360°

➝ x° + 75° + x° + 75° = 360°

➝ 2x + 150° = 360°

➝ 2x = 360 - 150

➝ 2x = 210

➝ x = 105°

Hence, The Angles Of Parallelogram Are 75°, 105°, 75°, 105° respectively.