Question

Two adjacent angles of a paralleogram are in the ratio 5: 4. Find the measures of all the
angles.
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Answer 1

Answer :

The measure of all angles of parallelogram are :-

• ∠A = 80°
• ∠B = 100°
• ∠C = 80°
• ∠D = 180°

Step-by-step explanation :-

To Find,

• The measure of all angles of parallelogram

Solution,

Given that,

• Two adjacent angles of a paralleogram are in the ratio 5 : 4

As we know that,

$\dag \: \: \: \underline{ \boxed{ \red{ \sf{Adjacent \: angles \: of \: parallelogram = {180}^{ \degree}}}}}$

Therefore,

Let us assume the parallelogram as ABCD, and the unknown adjacent angles as 5x and 4x,

[ 5x + 4x = 180° ]

➠ 5x + 4x = 180

➠ 9x = 180

➠ x = 180 / 9

➠ x = 20

The value of x is 20.

Now, let's find out the angles,

➻ 5x [ ∠B ]

➠ 5 × 20

➠ 100°

➻ 4x [ ∠A ]

➠ 4 × 20

➠ 80°

Therefore,

The measure of ∠C and ∠B,

• ∠C = ∠A .... opposite angles are equal.
• ∠B = ∠D .... opposite angles are equal.

The angles of parallelogram are :-

• ∠A = ∠C = 80°
• ∠B = ∠D = 100°.