The angles of a cyclic quadrilateral ABCD are
∠A = (6x + 10)°, ∠B = (5x)°
∠C = (x + y)°, ∠D = (3y – 10)°
Find x and y, and hence the values of the four angles.
NCERT Class X
Mathematics - Exemplar Problems
Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Answers
Answered by
429
According to the problem,
6x + 10 + x + y = 180
or, 7x + y = 170
or, y = 170 - 7x
Again, 5x + 3y - 10 = 180
or, 5x + 3y = 190
or, 5x + 3(170-7x) = 190
or, 5x + 510 - 21x = 190
or, -16x = -320
or, x = 20
So, y = 170 - 7x = 170 - 140 = 30
So, measure of all angles are 130°, 100°, 50°, 80°
6x + 10 + x + y = 180
or, 7x + y = 170
or, y = 170 - 7x
Again, 5x + 3y - 10 = 180
or, 5x + 3y = 190
or, 5x + 3(170-7x) = 190
or, 5x + 510 - 21x = 190
or, -16x = -320
or, x = 20
So, y = 170 - 7x = 170 - 140 = 30
So, measure of all angles are 130°, 100°, 50°, 80°
Answered by
46
Answer:
130,100,50,80
Step-by-step explanation:
Angle A: 6x+10 and Angle C : x+y
=6x+10+x+y
=7x+y=180-10
7x+y=170 therefore, y= 170-7x
And now Angle B: 5x and Angle D: 3y-10 on adding this
We get 5x+3y-10 = 180
5x+3y =190 on substuting y = 170-7x we get 5x + 3(170-7x)= 190
5x+ 510-21x= 190
-16x= -320( minus will be cancelled)
X=320/16 gives x= 20
Y= 170 -7×20
Y= 30
Therefore the angles are: 130,100,50,80
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