Question

One of the angles of the parallelogram is 75 degree. Find all the angles of parallelogram

Answer 1

Let's take the parallelogram as ABCD like in the attachment.

Given,

• $\angle{A}$ = 75°

To find,

• Remaining 3 angles

Then,

$\angle{A}$ + $\angle{B}$ = 180°

➝ 75° + $\angle{B}$ = 180°

➝ $\angle{B}$ = 180° - 75°

➝ $\angle{B}$ = 105°

.°. $\angle{B}$ = 105°

Why?

• The sum of the two adjacent angles of a parralelogram is 180°.

Now,

$\angle{A}$ = $\angle{C}$

→ 75° = 75°

.°. $\angle{C}$ = 75°

Why?

• The opposite angles of a parralelogram is equal.

Here,

$\angle{B}$ = $\angle{D}$

➙ 105° = 105°

.°. $\angle{D}$ = 105°

Why?

• The opposite angles of parralelogram is equal.

Hence, $\angle{A}$ = 75°, $\angle{B}$ = 105° $\angle{C}$ = 75° $\angle{D}$ = 105° are the angles of the parralelogram.