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 800 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 200 less then three times the smaller, then the angles are :-
In the given figure, ∠BAC = 400, ∠ACB = 900 and ∠BED = 1000, 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 = 500, then ∠2 is equal to –
In a right-angled 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
∠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 = 500, then ∠BOC = ?
a+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= 180-65= 115
An exterior angle of a triangle is 800 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.
So the angles are
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)
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 = 500 and ∠ECD = 600, 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 = 1800 (corresponding angles)
∠ECD = 180 - 150 = 300
since AB || CD so
∠ABC= ∠BCD (alternate interior angles)
∠ABC = 30 + ∠ECD = 30 + 30 = 600
In the adjoining figure, the bisectors of ∠CBD and ∠BCE meet at the point O. If ∠BAC = 700, then ∠BOC is equal to :-
In the given figure, ∠OEB = 750, ∠OBE = 550 and ∠OCD = 1000. 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 = 250, then ∠BAC is equal to :-
Find the angle if six times of its complement 12° less than twice of its supplement?