find the angles of a,b,c,d
Answers
Answer:
c = 83 (vertically opposite angle)
79 + a= 180 (linear pair)
a= 180-79
a= 101 degrees
a +b= 180 (co-interior angles)
101+ b= 180
b = 180-101
b=79 degrees
d+ c= 180 (co- interior angles)
d+ 83= 180
d= 180-83
d= 97 degrees
therefore, a= 101 degrees, b= 79 degrees, c= 83 degrees, d= 97 degrees
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Given : A Quadrilateral with one pair of lines parallel
To Find : Angles a , b , c and d
Solution:
"Linear pair of angles adds up to 180°"
angle a and 79° forms a linear pair.
Hence a + 79° = 180°
=> a = 101°
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent. ( Equal in Measure)
• Alternate angles are congruent. ( Interiors & Exterior both )
• Co-Interior angles are supplementary. ( adds up to 180°)
∠b = 79° ( corresponding angles)
∠c = 83° ( vertically opposite angles are equal )
∠c + ∠d = 180° ( Co-Interior angles )
Substitute ∠c = 83°
83° + ∠d = 180°
∠d = 97°
Measure of a , b , c and d are 101° , 79° , 83° and 97° respectively.
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