Question

the measure of two adjacent angles of llgm are in the ratio 4:5 find the measure of each angle​

Answer 1

Answer:

$\huge\tt{\boxed{\underbrace{\overbrace{\bold\color{lime}{Solution:}}}}}$

Given:

• The measure of two adjacent angles of llgm are in the ratio 4:5

To find:

• The measure of each angle

$\huge\underbrace\mathfrak\color{lime}{ †\: Solution:–}$

$let \: a = 4x$

$b = 2x$

$\sf{\boxed{\orange{\bold{ ∠A\:+∠B\:=180}}}}$

$\green{ \underline{ \sf{Adjacent\: angles: Supplementary}}}$

• Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x

∠A+∠B=180°

=>4x+5x=180°

=>9x=180°

=>x=180/9

=>x=20°

• ∠A=4x=4×20=80°
• ∠B=5x=5×20=100°

Also ∠B+∠C=180° [Since ∠B and ∠C are adjacent angles]

=>100 +∠C=180°

=>∠C=180°-100°

=80°

Now, ∠C+∠D=180°[Since ∠C and

∠D are adjacent angles]

=>80° +∠D=180°

=>∠D=180°−80°

=100°