Question

Two opposite angles of a parallelogram are 6x-170

and x+630

. Find the measure of each

angle of the parallelogram.​

Answer 1

$\Large{\underline{\bf{Given:}}}$

✒️ Two Opposite Angles of a Parallelogram are (6x-170)° and (x+630)°

$\Large{\underline{\bf{To\;Find:}}}$

☞ Measure of each angle of the Parallelogram.

$\huge{\underline{\underline{\bf{Solution:}}}}$

Let, ABCD is the Parallelogram

∠DAB = 6x-170° & ∠DCB = x+630°

W.K.T

✯ Opposite Angles of Parallelogram are Equal

☞ ∠DAB = ∠DCB & ∠ABC = ∠ADC

$→\;{\sf{∠DAB = ∠DCB}}$

$→\;{\sf{6x-17° = x+63°}}$

$→\;{\sf{6x-x = 63+17}}$

$→\;{\sf{5x = 80}}$

$→\;{\sf{x = \frac{80}{5}}}$

$→\;{\sf{x = 16}}$

∠DAB = 6(16)-17 ➝ 79°

∠DCB = 16+63 ➝ 79°

W.K.T

✯ Adjacent Angles of Parallelogram are Supplementary.

$→\;{\sf{∠ABC + ∠DCB = 180°}}$

$→\;{\sf{∠ABC = 180°-79°}}$

$→\;{\sf{∠ABC = 101°}}$

So, ∠ABC = ∠ADC = 101°

$\Large{\green{\underline{\underline{\mathfrak{AnSweR:}}}}}$

All The Angles of Parallelogram are

$◕➜\;\huge{\red{\mathfrak{79°,101°,79°,101°}}}$

Hope It Helps You ✌️