Triangles - Study Mode

[#151] In a ΔABC, BC is extended upto D
∠ACD = 120°, ∠B = $$frac{1}{2}$$ ∠A, then ∠A is:
Correct Answer

(C) 80°

Explanation

Solution: ∠C = 180° - 120° = 60° ∠A + ∠B + ∠C = 180° ∠A + $$frac{1}{2}$$ ∠A + 60° = 180° $$frac{3}{2}$$ ∠A = 120° ∠A = 80°

[#152] In ΔABC, ∠B = 60° and ∠C = 40°
AD and AE are respectively the bisector of ∠A and perpendicular on BC. The measure of ∠EAD is:
Correct Answer

(C) 10°

Explanation

Solution: As we know $$eqalign{
& angle EAD = frac{{angle B - angle C}}{2} cr
& angle EAD = frac{{60 - 40}}{2} cr
& angle EAD = {10^ circ } cr} $$

[#153] In a right angled ΔABC, ∠ABC = 90°, AB = 3, BC = 4, CA = 5
BN is perpendicular to AC, AN : NC is
Correct Answer

(B) 9 : 16

Explanation

Solution: According to question, Given : ∠ABC = 90° $$frac{{AN}}{{NC}} = ?$$ ΔABC ∼ ΔBNC ΔABC ∼ ΔANB ∴ ΔABC ∼ ΔBNC ∼ ΔANB AB = 3, BC = 4, AC = 5 $$eqalign{
& frac{{AB}}{{BN}} = frac{{AC}}{{BC}} cr
& BN = frac{{AB imes BC}}{{AC}} = frac{{3 imes 4}}{5} = 2.4 cr
& frac{{BC}}{{NC}} = frac{{AB}}{{NB}} cr
& frac{4}{{NC}} = frac{3}{{2.4}} cr
& NC = 3.2 cr
& frac{{AB}}{{AN}} = frac{{BC}}{{NB}},,,,,,,,,,,,,frac{3}{{AN}} = frac{4}{{2.4}} cr
& AN = 1.8 cr
& frac{{AN}}{{NC}} = frac{{1.8}}{{3.2}} cr
& frac{{AN}}{{NC}} = frac{9}{{16}} cr
& herefore AN:NC = 9:16 cr} $$