In the given figure, CE ⊥ AB, ∠BCE = 20° and ∠BAD = 50°, Find ∠BDA :
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Solution
∠EBC = 180° – 90° – 20° = 70° = ∠ABD
∠BDA = 180° – (70° + 50°) = 60°
In ∆ABC, AC = 5 cm, AD = 3 cm, BD = 7 cm and DE || BC, then calculate the length of AE ?
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Solution
By the mid point theorem
⇒
⇒ 15 – 3 AE = 7 AE ⇒ AE = = 1.5 cm
What is the ratio of side and height of an equilateral triangle?
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Solution
AB2 = BD2 + AD2
a2 = h2 +
⇒ h2 =
In the figure ∆ABC, ∠BCA = 120° and AB = c, BC = a, AC = b, then :
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Solution
cos c =
c2 = a2 + b2 + ab
In the given diagram of ∆ABC, ∠B = 80°, ∠C = 30°. BF and CF are the angle bisectors of ∠CBD and ∠BCE respectively. Find the value of ∠BFC
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Solution
∠BFC = 90° –
= 90° –
If a, b, c are three sides of a triangle ∆ABC and c is the largest side, then ∆ABC is obtuse triangle if –
The suplement of 123° 45′ is –
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Solution
123° 45' + X = 180° = 179° 60'
X = 179° 60' - 123° 45'
X = 56° 15'
AB || CD, show in the figure. Find the value of x :
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Solution
X + 10° = (180° - 100°) + 30°
⇒ X = 100°
In the given figure XY || PQ. Find the value of x.
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Solution
∠BAO = 180° - (60° + 35°) = 85°
∠AOB = 180° - (85° + 20°) = 75°
The area of a sector of a circle of radius 8 cm, formed by an arc of length 5.6 cm is-
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Solution
Area of sector = Arc × radius
= ×8×5.6 = 22.4 cm2