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

1.	One of the angles of a parallelogram is 75 degrees. Find the measures of the remaining angles of the parallelogram
Answer» ✬ 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° $\large\boxed{\texttt{Verified}}$

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

Answer»

✬ ANGLES = 105° , 105° , 75° ✬

Step-by-step explanation:

Given:

To Find:

Solution: LET GFEX be a parallelogram where

Let other pair of OPPOSITE angles be of x°.

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

★ 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°

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