Question

AB is a diameter of a circle with centre O.If angle BAE=70, angle BAC=70, angle ACD=30 and angle BAE=60, find angle BAC, angle ACD and angle ABE

Answer 1

HEY MATE,
WELCOME TO THE CONCEPT OF “CIRCLE”

Formulas that are used in the solution are:

⇒Sum of opposite angles in a cyclic quadrilateral = 180°

⇒Angle in a semicircle = 90°

⇒Sum of angles in a triangle =180°

《ANSWER IN THE ABOVE ATTACHMENT》

Answer 2

Answer:

Angle BAC = 110, angle ACD = 30, and angle ABE = 50

Step-by-step explanation:

From the above question,

Given that AB is a diameter of a circle with center O, and that,

angle BAE = 70, angle BAC = 70, angle ACD = 30, and angle BAE = 60.

We can use the property of cyclic quadrilaterals to find the angles. In a cyclic quadrilateral, the opposite angles add up to 180 degrees.

Using this property, we have:

Angle BAE + Angle BAC = 180 (opposite angles in a cyclic quadrilateral)

Angle ACD + Angle BAE = 180 (opposite angles in a cyclic quadrilateral)

Substituting the given angles, we get:

70 + Angle BAC = 180

30 + 60 = 90

Solving for Angle BAC and Angle ACD, we get:

Angle BAC = 180 - 70 = 110

Angle ACD = 90 - 60 = 30

Finally, to find angle ABE, we can use the property that the sum of the angles in a triangle is 180 degrees.

Given that angle BAE = 70, angle BAC = 110, and angle BAE = 60, we have:

70 + Angle ABE + 60 = 180

Solving for Angle ABE, we get:

Angle ABE = 180 - 70 - 60 = 50

Therefore, angle BAC = 110, angle ACD = 30, and angle ABE = 50.

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