O केंद्र वाले वृत्त में ABCD एक चतुर्भुज है। यदि `angleCOD=120^(@)` तथा `angleBAC=30^(@)` है।, तब `angleBCD` है।

Options

A. `75^(@)`
B. `90^(@)`
C. `120^(@)`
D. `60^(@)`

Answer

C

Explanation

According to question,
ABCD is cyclic quadrilateral with center O.
ABCD एक चक्रीय चतुर्भुज हैं जिसका केंद्र O हैं

Given,
`angleCOD=120^(@)`
`angleBAC=30^(@)`
`angleBCD=?`
`angleCAD=1/2angleCOD`
`angleCAD=1/2 xx 120^(@) = 60^(@)`
`angleBAD=30^(@)+60^(@)=90^(@)`
Note: In cyclic quadrilateral sum of opposite angles is `180^(@)`
`angleBAD + angleBCD= 180^(@)`
`angleBCD=180^(@)-90^(@)`
`angleBCD=90^(@)`