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.
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Answered by
4
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°
Answered by
0
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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