Question

7. C is point on the minor arc AE of the circle with centre O. Given
angle ACE = x°, angle AOE= yº and express y in terms of x. Calculate x, if
ACEO is a parallelogram.​

Answer 1

In the diagram take B as E.

Step-by-step explanation:

clearly, major arc AE subtends x° at a point on the remaining part of the circle.

therefore reflex AOE = 2x

= 360° - y° =2x

y° = 360° - 2x

thus, y = 360 - 2x

if ACEO is a parallelogram, then

x°=y° i.e. x=y

x° = 360°-2x = 3x = 360°

x = 120°

hope it helps.

Answer 2

(Please note that that there are some mistakes in the question. Please refer to the question written below)

C is a point on the minor arc AB of the circle with centre O. Given

angle ACB = x°, angle AOB yº and express y in terms of x. Calculate x, if

ACBO is a parallelogram.​

________________

Major arc AB subtends $\sf x \°$ at a point on the remaining part of the circle.

$\sf \therefore reflex \: \angle AOB = 2x\°$

$\sf y\° = 360\°-2x\°$ ...(i)

If ACBO is a paralelloram, then

$\sf x\° = y\°$ , i.e., $\sf x=y$

$\sf x\°= 360\° -2x \implies 3x =360\°$

$\boxed{\sf{x\° = 120\°}}$