Mathematics
In the given figure, AD = BD, then angle ACD is :
43°
22°
65°
28°
Triangles
16 Likes
Answer
Given,
AD = BD
In △ ABD,
⇒ ∠BAD = ∠ABD = 65° (Angles opposite to equal sides are equal)
In △ ABC,
⇒ ∠BAC = ∠BAD + ∠DAC = 65° + 22° = 87°.
By angle sum property of triangle,
⇒ ∠BAC + ∠ACB + ∠CBA = 180°
⇒ 87° + ∠ACB + 65° = 180°
⇒ ∠ACB + 152° = 180°
⇒ ∠ACB = 180° - 152° = 28°.
From figure,
⇒ ∠ACD = ∠ACB = 28°.
Hence, Option 4 is the correct option.
Answered By
10 Likes
Related Questions
In the given figure, ∠B = ∠C and ∠BAD = ∠CAD, then :
AB = AC
AB ≠ AC
∠ADB ≠ ∠ADC
∠ADB ≠ 90°
In the given figure, AD ⊥ BC and AB = AC, then :
△ ABD ≇ △ ACD
BD = CD
∠BAC = 90°
∠CAD = 45°
In the given figure; BE = DC, then :
AD = DC
AE = BE
AD = AE
∠ABE = ∠DAC
In △ ABC and △ PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q; then triangles are :
isosceles but not congruent
isosceles and congruent
congruent but not isosceles
neither isosceles nor congruent.