Maths / Circles / Angles in the Same Segment are Equal

QUESTION

 AB is the diameter of the given circle with centre O. If $\angle BAD=35^o,$ what is the measure of $\angle ACD\;?$

 OPTIONS A. $55^o$ B. $35^o$ C. $125i^o$ D. $145^o$
Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

AB is the diameter of the given circle with centre O. $\angle BAD=35^o,$

$\angle ADB\;= 90^0\;\;\;\;\;\;\; [angle \;in\;the\semicircle\;is\90^0]$

$In\Delta ABD \;\;\;\angle BAD+ \angle ADB+ \angle ABD = 180^0\;\;\;\;\;\;\; [angle \;sum\;property]$​​​​​​

$35^0 + 90^0 + \angle ABD = 180^0$

$125^0 + \angle ABD = 180^0$

$\angle ABD = 180^0-125^0= 55^0$

$\angle ACD=\angle ABD=55^0\;\;\;\;\;\;\[Angles\;in\;the\;same\;segment\;are\;equal]$

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