Question : ABCD is a cyclic quadrilateral and BC is the diameter of the related circle on which A and D also lie. $\angle \mathrm{BCA}=19°$ and $\angle \mathrm{CAD}=32°$. What is the measure of $\angle \mathrm{ACD}$?
Option 1: 41°
Option 2: 38°
Option 3: 40°
Option 4: 39°
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Correct Answer: 39°
Solution : Given, $\angle{CAD}=32°$ and $\angle{BCA}=19°$ We know, that the angle formed by the diameter is 90°. ⇒ $\angle{BAC}=90°$ The sum of the opposite angle of a quadrilateral = 180°. ⇒ $\angle{CAD}+\angle{BAC}+\angle{BCA}+\angle{ACD}=180°$ ⇒ $32°+90°+19°+\angle{ACD}=180°$ ⇒ $141°+\angle{ACD}=180°$ ⇒ $\angle{ACD}=180°-141°$ ⇒ $\angle{ACD}=39°$ Hence, the correct answer is 39°.
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Question : ABCD is a cyclic quadrilateral and BC is the diameter of the circle. If $\angle D B C=29^{\circ}$, then $\angle B A D=$?
Option 1: 129°
Option 2: 119°
Option 3: 111°
Option 4: 122°
Question : PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If $\angle RPQ=38°$, what is the value (in degree) of $\angle PSR$?
Option 1: 52°
Option 2: 77°
Option 3: 128°
Option 4: 142°
Question : ABCD is a rhombus with $\angle$ABC = 52°. The measure of $\angle$ACD is:
Option 1: 54°
Option 2: 26°
Option 3: 48°
Option 4: 64°
Question : In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If $\angle XBC=82°$ and $\angle ADB=47°$, then the value of $\angle BDC$ is:
Option 1: 40°
Option 2: 35°
Option 3: 30°
Option 4: 25°
Question : AB is the diameter of a circle with centre O. If P is a point on the circle such that $\angle$AOP=110°, then the measure of $\angle$OBP is:
Option 1: 50°
Option 2: 65°
Option 3: 60°
Option 4: 55°
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