Plane Geometry
- The sum of two angles of a triangle is 116° and their difference is 24°. The measure of the smallest angle of the triangle is :
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Let three angles of triangle = p, q and r
According to the question,
p + q = 116°
p – q = 24
On adding, we get
2p = 116 + 24 = 140⇒ p = 140 = 70° 2
∴ p + q = 116°
⇒ 70° + q = 116°
Correct Option: C
Let three angles of triangle = p, q and r
According to the question,
p + q = 116°
p – q = 24
On adding, we get
2p = 116 + 24 = 140⇒ p = 140 = 70° 2
∴ p + q = 116°
⇒ 70° + q = 116°
∴ q = 116° – 70° = 46°
Third angle (r) = 180° – 116° = 64°
- The difference between the largest and the smallest angles of a triangle whose angles are in the ratio of 5 : 3 : 10 is
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On the basis of given question , we have
In ∆ABC,
A : B : C = 5 : 3 : 10
We know that sum of all three angles of triangle is 180°
i.e. ∠A + ∠B + ∠C = 180°
Sum of the terms of ratio = 5 + 3 + 10 = 18Correct Option: D
On the basis of given question , we have
In ∆ABC,
A : B : C = 5 : 3 : 10
We know that sum of all three angles of triangle is 180°
i.e. ∠A + ∠B + ∠C = 180°
Sum of the terms of ratio = 5 + 3 + 10 = 18∴ Required difference = 
10 - 3 
× 180 = 70° 18
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In an acute–angled triangle ABC if sin (B + C – A) = √3 and tan (C + A – B) = 1, then C is equal to 2
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As per the given question ,
Sin (B + C – A) = √3 = sin 60° 2
⇒ B + C – A = 60° ..... (i)
Again,
tan (C + A – B) = 1 = tan 45°
⇒ C + A – B = 45° ..... (ii)
On adding (i) and (ii) , we get
∴ B + C – A + C + A – B = 60° + 45°
Correct Option: C
As per the given question ,
Sin (B + C – A) = √3 = sin 60° 2
⇒ B + C – A = 60° ..... (i)
Again,
tan (C + A – B) = 1 = tan 45°
⇒ C + A – B = 45° ..... (ii)
On adding (i) and (ii) , we get
∴ B + C – A + C + A – B = 60° + 45°
⇒ 2C = 105°⇒ C = 105° = 52.5° 2
- In a triangle XYZ, which of the following conditions is true?
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On the basis of question ,
The difference between two sides of a triangle is less than the third side.Correct Option: C
On the basis of question ,
The difference between two sides of a triangle is less than the third side.
∴ In ∆XYZ,
XY – YZ < XZ
- In ∆ ABC, if ∠BAC = 90° and AB = AC, then ∠ABC is :
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As per the given in question , we draw a figure triangle ABC
Given , AB = AC and ∠BAC = 90°Correct Option: C
As per the given in question , we draw a figure triangle ABC
Given , AB = AC and ∠BAC = 90°∴ ∠ABC = ∠ACB = 90° = 45° 2
