in the figure AB is a diameter of a semicircle. three angles x, y, z are marked outside on the semicircle and inside the semicircle.
a. what is the value of y?
b. if x, y, z are in an arithmetic sequence, then what is x+2
c. if the common difference of the sequence is 50 then find x and z
Answers
) (1) Write with reason, which of the following are finite or infinite: A = {xlx is a multiple of 3) (ii) B=(yly is a factor of 13) (iii) C = {..., -3, -2, -1,0) (iv) D-xlx=2", n EN)
Given: In the figure, AB is a diameter of a semicircle. Three angles x, y, z are marked outside on the semicircle and inside the semicircle.
To find:
a. The value of y.
b. If x, y, z are in an arithmetic sequence, then what is x+2.
c. If the common difference of the sequence is 50, then find x and z
Solution:
a.
As clear from the figure, angle y is equal to 90°. The points B, C and P form a right-angled triangle.
b.
Since y is 90°, the value of x must be 60° and the value of z must be 120°. So x, y and z are in arithmetic sequence with a common difference equal to 30°. The value of x is 60 so (x+2) would be 62.
c.
If the common difference of the sequence is 50, x and y can be calculated as follows.
x = 90 - 50
= 40°
z = 90 + 50
= 140°
Therefore,
a. The value of y is 90°.
b. (x+2) is 62.
c. x is 40° and y is 140°.