In ,∆ ABC , \angleB=60^\circ and \angleC=40^\circ, AD and AE are respectively the bisector of \angleA and perpendicular onBC. The measure of \angleEAD is:

SSC CHSL 6 Dec 2015 Shift 2 Paper

Question : 101 of 200

Marks: +1, -0

In ,

∆ ABC , ∠B=60°

and

∠C=40°

, AD and AE are respectively the bisector of

∠A

and perpendicular onBC. The measure of

∠EAD

is:

Solution:

Given : AD is angle bisector of ∠ A and AE is perpendicular to BC.
To find : ∠ EAD = ?
In ∆ ABC,
⇒

∠A+ ∠B+ ∠C= 180°

⇒

∠ 60°+ 40°=180°

⇒

∠A = 180°− 100 °= 80°

∵

∠BAD =∠CAD

⇒

∠CAD = 80/2=40°

Using external angle property, ⇒

∠ADE = ∠CAD + ∠C

⇒

∠ADE=40°+ 40° = 80°

∴ In ∆ EAD,
⇒

∠EAD+ ∠ADE+ ∠DEA= 180°

⇒

∠EAD+ 80°+ 90° = 180°

⇒

∠EAD=180°-170°=10°

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