`DeltaABC` में, BC को D तक बढ़ाया गया, तथा CD=AC यदि `angleBAD=111^(@)` तथा `angleACB=80^(@)` हे, तब `anglePRQ` का मान ज्ञात करे?

Options

A. `31^(@)`
B. `33^(@)`
C. `35^(@)`
D. `29^(@)`

Answer

D

Explanation

According to question,

Given, AC=CD
`angleBAD=111^(@)`
`angleACB=80^(@)`
`therefore angleACD=180^(@)-80^(@)`
`angleACD=100^(@)`
In isosceles triangle ACD
`angleACD+angleCAD+angleADC=180^(@)`
`2angleCAD = 180^(@)-100^(@)`
`therefore angleCAB=111^(@)-40^(@)=71^(@)`
`therefore angleABC=180^(@)-71^(@)-80^(@)`
`angleABC=29^(@)`