Q. 75.0( 2 Votes )

Two opposite angles of a parallelogram are (3x-2)o and (50-x)o. The measures of all its angles are
A. 97°, 83°, 97°, 83°

B. 37°, 143°, 37°, 143°

C. 76°, 104°, 76°, 104°

D. none of these

Answer :

To Find: All angles of a parallelogram
Given: Opposite angles are (3x - 2) and (50 - x)
Diagram:

Let the parallelogram be ABCD, and opposite angles be ∠B and ∠D, such that
∠A = (3x - 2)
∠C = (50 - x)

∠B = ∠D (Opposite angles of a parallelogram are equal)

3x - 2 = 50 - x

3x + x = 50 + 2

4x = 52°

x = 13°

Putting the value of x, we get,
∠B = 3(13) - 2 = 37°
∠D = 50 - 13 = 37°
Also. 
∠A = ∠C         (Opposite angles of a parallelogram are equal)
By angle sum property of quadrilateral,
∠A + ∠B + ∠C + ∠D = 360°
37° + ∠A + 37° + ∠C = 360°
2∠A + 74 =360°
2∠A = 286°
∠A = 143°
Hence, 
∠A = ∠C =143°

So, Angles of parallelogram is 37°, 143°, 37° and 143°.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
QuadrilateralsQuadrilateralsQuadrilaterals32 mins
Members of QuadrilateralsMembers of QuadrilateralsMembers of Quadrilaterals65 mins
Genius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding Quadrilaterals20 mins
Quiz | Polygon & their PropertiesQuiz | Polygon & their PropertiesQuiz | Polygon & their Properties46 mins
Champ Quiz | Polygons (Quadrilaterals)Champ Quiz | Polygons (Quadrilaterals)Champ Quiz | Polygons (Quadrilaterals)30 mins
NCERT |  Discussion on Imp. Qs. of  QuadrilateralsNCERT |  Discussion on Imp. Qs. of  QuadrilateralsNCERT | Discussion on Imp. Qs. of Quadrilaterals43 mins
NCERT | Standard Form of NumbersNCERT | Standard Form of NumbersNCERT | Standard Form of Numbers41 mins
Champ Quiz | Spelling of important wordsChamp Quiz | Spelling of important wordsChamp Quiz | Spelling of important words47 mins
Metals of SurprisesMetals of SurprisesMetals of Surprises38 mins
Quiz on Mystery of OnionQuiz on Mystery of OnionQuiz on Mystery of Onion30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses