Question

if two opposite angles of a parallelogram are (63-3x) and (4x-7) find all angles of the parallelogram

Answer 1

We know that in a parallelogram, opposite angles are always equal

This means that (63-3x) = (4x-7)   {It is given that they are opposite angles}

63 - 3x = 4x -7
⇒ 63 + 7 = 4x + 3x
⇒ 70 = 7x
⇒ x = 10

Now, substituting x= 10 in (63 - 3x), we get

⇒( 63 - 30) = 33°

Hence the two angles are 33°

Let one angle be y

We know that the adjacent angles are supplementary

∴  33°+y =180°
y =180°-33°
y =147°.

So the angles of the parallelogram are 33°, 33°, 147° and 147°

Answer 2

Hey there!

if two opposite angles of a parallelogram are (63-3x) and (4x-7) find all angles of the parallelogram

According to the property of parellelogram, Opposite sides are equal.

that is,
$(63 - 3x) = (4x - 7)$

$63 + 7 = 4x + 3x$

$70 = 7x$

$x = \frac{70}{7}$

$x = 10$

First angle =
(substitute value of x= 10)

$(63 - 3x)$

$63 - 3 \times 10$

$63 - 30$

$33$

If we take two adjacent angles, one angle is 33° then the other angle (y) = ?

Adjacent angles are supplementary

$33 + y = 180$

$y = 180 - 33$

$y = 147$

Hence, the four angles of parellelogram are :

147°, 147°, 33°,33°

Hope helped.qQ