किसी त्रिभुज `DeltaABC` में, `angleB=60^(@)` , `angleC=40^(@)` है यदि AD तथा AE क्रमश: `angleA` के आतंरिक समद्विभाजक तथा BC पर लंबवत है| `angleDAE` ज्ञात करे?

Options

A. `5^(@)`
B. `10^(@)`
C. `40^(@)`
D. `60^(@)`

Answer

B

Explanation

According to question,

Given: `angleB = 60^(@)`
`angleC=40^(@)`
As we know that
`angleA+angleB+angleC=180^(@)`
`angleA=180^(@)-60^(@)-40^(@)`
As we know at
`angleA+angleB+angleC=180^(@)`
`angleA=180^(@)-60^(@)-40^(@)`
`therefore angleBAD=80^(@)/2=40^(@)`
In `Delta AEB`
`angleA + angleB+ angleE=180^(@)`
`angleA= 180^(@)-60^(@)-90^(@)`
`angleA = 30^(@)`
Then, `angleDAE = angleDAB= angleEAB`
`40-30`
`angleDAE= 10^(@)`
By trick:
`angleDAC = (angleB-angleC)/(2)`
`=(60^(@)-40^(@))/2=10^(@)`