An exterior angle of a triangle is 80^{°}and two interior opposite angles are equal. Measure of each of these angles is :
Exterior angle = sum of two interior opposite angle so, exterior angle =1/2×80 = 40^{°}
An exterior angle of a triangle is 80^{0} and the interior opposite angles are in the ratio 1 : 3. Measure of each interior opposite angle is :
In the adjoining figure, if m ║ n, then ∠4 + ∠7 is equal to –
If two angles are supplementary and the larger is 20^{0} less then three times the smaller, then the angles are :
In the given figure, ∠BAC = 40^{0}, ∠ACB = 90^{0} and ∠BED = 100^{0}, Then ∠BDE = ?
The angle which is equal to 8 times its complement is :
Two planes intersect each other to form a :
In the adjoining figure, m ║ n, if ∠1 = 50^{0}, then ∠2 is equal to –
In a rightangled triangle where angle A = 90° and AB = AC. What are the values of angle B?
∵ In ∆ABC,
AB = AC
∴ ∠B = ∠C ...(1)
 Angles opposite to equal sides of a triangle are equal
In ∆ABC,
∠A + ∠B + ∠C = 180°
 Sum of all the angles of a triangle is 180°
⇒ 90° + ∠B + ∠C = 180°
 ∵ ∠A = 90° (given)
⇒ ∠B + ∠C = 90° ...(2)
From (1) and (2), we get
∠B = ∠C = 45°.
In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50^{0}, then ∠BOC = ?
a+b+c = 180
50+b+c= 180
b+c = 130 ............(1)
divide equation (1) by 2
1/2(b+c) = 65...........(2)
now in triangle obc
o+1/2(b+c) = 180
o+65= 180 ( from (2))
o= 18065= 115
An exterior angle of a triangle is 80^{0} and the interior opposite angles are in the ratio 1 : 3. Measure of each inte4rior opposite angle is :
Let the interior angles be x and 3x
We know that exterior angle of triangle is equal to sum of interior opposite angles.
⇒ x+3x=80^{∘}
⇒ 4x=80^{∘}
⇒ x=20^{∘}
So the angles are
x=20^{∘}
3x=3×20^{∘}
= 60∘
In figure, AB and CD are parallel to each other. The value of x is :
In the adjoining figure, m ║ n. If ∠a : ∠b = 2 : 3, then the measure of ∠h is –
A+b =180(linear pair)
2x+3x=180
5x=180
x=180/5
x=36
a=2x=2*36=72
b=3x=3*36=108
b=d (vertical opposite angles are equal)
d=f (alternative interior angles are equal)
f=h (vertically opposite angles are equal)
So, h= 108
In the given figure, the measure of ∠ABC is :
In the given figure, AB ∥ CD. If ∠EAB = 50^{0} and ∠ECD = 60^{0}, then ∠AEB = ?
In the given figure, the value of x which makes POQ a straight line is :
In two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the smaller of the two angles is :
In the adjoining figure, AB ║ CD and AB ║ EF. The value of x is :
Given, AB ║ CD and AB ║ EF
so CD  EF
which means ∠ECD + ∠CEF = 180^{0} (corresponding angles)
∠ECD = 180  150 = 30^{0}
since AB  CD so
∠ABC= ∠BCD (alternate interior angles)
∠ABC = 30 + ∠ECD = 30 + 30 = 60^{0}
In the adjoining figure, the bisectors of ∠CBD and ∠BCE meet at the point O. If ∠BAC = 70^{0}, then ∠BOC is equal to :
In the given figure, ∠OEB = 75^{0}, ∠OBE = 55^{0} and ∠OCD = 100^{0}. Then ∠ODC = ?
If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the largest of two angles is :
Sum of all angles around a main point equals to
What is the supplement of 105°
In the adjoining figure, BE and CE are bisectors of ∠ABC and ∠ACD respectively. If ∠BEC = 25^{0}, then ∠BAC is equal to :
Find the angle if six times of its complement 12° less than twice of its supplement?
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