Question

please solve the following sum of chapter circles

Answer 1

Question :

In the given figure CE is a tangent to the circle at point C. ABCD is a cyclic quadrilateral. If ∠ABC = 93° and ∠DCE = 35°. Find :

• ∠ADC
• ∠CAD
• ∠ACD

Given :

• ∠ABC = 93°
• ∠DCE = 35°
• ABCD is a cyclic quadrilateral

To find :

• ∠ADC
• ∠CAD
• ∠ACD

According to the question,

i) ∠ACD

➝ ∠ABC + ∠ACD = 180°

Reason : Property of cyclic quadrilateral

➝ 93° + ∠ACD = 180°

➝ ∠ACD = 180° - 93°

➝ ∠ADC = 87°

ii) ∠CAD

➝ ∠ACD + ∠CAD = 35°

Reason : Sum of two interior angle = Exterior angle

➝ 87° + ∠CAD = 35°

➝ 87° - 35° = ∠CAD

➝ 52° = ∠CAD

iii) ∠ACD

➝ ∠CAD + ∠ADC + ∠ACD = 180°

Reason : Angle sum property

➝ 52° + 87° + ∠ACD = 180°

➝ 139° + ∠ACD = 180°

➝ ∠ACD = 180° - 139°

➝ ∠ACD = 41°

So,

• ∠ADC = 87°
• ∠CAD = 52°
• ∠ACD = 41°

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