Question

Exercise 3.3 A) The adjacent angles of a parallelogram are in the ratio 1: 3. Then find all the interior angles of a parallelogram.​

Answer 1

Answer:

All four angles of are 45° , 135° , 45° and 135°

Step-by-step explanation:

Let two angles are X and 3X.

As we know that sum of two adjacent angles of a parallelogram is 180°.

So,

X + 3X = 180

4X = 180

X = 180/4 = 45°

First angle = X = 45°

and,

Second angle = 3X = 3 × 45 = 135°.

Therefore,

Let two angles are X and 3X.

All four angles of are 45° , 135° , 45° and 135°

Answer 2

Answer:

.

Step-by-step explanation:

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180 ⁰

⇒1x+3x=180 ⁰

⇒4x=180 ⁰

⇒x= 180 ⁰ / 4

x = 45

∴∠1×45 ⁰

= 45⁰

and, ∠B=3×45⁰

= 135⁰

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A= 45 ⁰

and ∠D=∠B=135 ⁰

Hence, ∠A=45 ⁰

,∠B=135⁰

,∠C=45 ⁰

and ∠D=135 ⁰

Hence proved

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