1 Crore+ students have signed up on EduRev. Have you? 
If one angle of the triangle is equal to the sum of the other two angles then the triangle is
Let the angles of triangle be x, y and
180°  ( x + y)
∴ 180°  (x + y) = (x + y)
⇒ 2(x + y) = 180°
⇒ x + y = 90°
∴ (180° (x + y)) = 180°  90° = 90°
∴ The triangle will be right angled triangle
Constructing a line PQ  BC,
∠APQ = ∠ABC = 55°
∵ ∠AQL is an exterior angle for ∠APQ
∴ ∠APQ + 25° = a
⇒ a = 25° + 55° = 80°
b = 70° (Alternate opposite ∠s)
∴ x = a + b = 70° + 80° = 150°
If the bisectors of the acute angles of a right triangle meet at O, then the angle between the two bisectors at O is equal to:
∠AOC = 90º + 1/2∠B
= 90º + 1/2 x 90º
= 90º + 45º
= 135º
Find x if BO and CO are the bisected of exterior angles at B and C respectively.
x = 90°  1/2∠A
= 90°  1/2 x 70°
= 90°  35° = 55°
The value of x from the adjoining figure will be:
x = 90° + 1/2∠A
= 90° + 1/2 x 72°
= 90° + 36°
= 126°
AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65° then
∠APR + ∠CQF = 65°
(corresponding ∠s)
∠APR + ∠OPQ = 65°
⇒ 25° + Q = 65°
⇒ Q = 40°
∵ ∠OQF is on exterior angle for ∠POQ
∴ q + ∠POQ = 65° + 30°
⇒ p + q = 65°
⇒ p = 95°  40° = 55°
The value of x from the adjoining figure will be:
∠ABC + ∠A = ∠ACD
⇒ ∠ACD = ∠ABC + 84°
⇒ ∠ECD = ∠EBC + 42° ...(i)
∵ ∠ECD is an exterior angle for ∠EBC
∴ ∠ECD =∠EBC = x ...(ii)
Comparing (i) and (ii), we get
x = 42°
ABC is a triangle in which ∠B = 2∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is
In Δs ABC and DCE
∠ABE = ∠DCE = ∠B/2
AB = CD (given)
BE = CE (∵ ∠ABE =∠DCE = ∠B/2)
∴ ΔABE ≅ ΔDCE [ By SSS congruence]
ABCD is a quadrilateral having AC as a diagonal, then
In ΔABC
AB + BC > AC ...(i)
In ΔADC,
AD + DC > AC ...(ii)
Using (i) and (ii)
CD + AD + AB + BC > 2AC
In ΔABC, AC >AB and AD is the bisector of ∠A. Then
In ΔABC,
∵ AC > AB
∴ ∠ABC = ∠ACB
⇒  ∠ABC  ∠ACB
⇒ 180°  ∠ABC < 180°  ∠ACB
⇒ 180°  ∠ABC  x < 180°  ∠ACB  x
⇒ ∠ADB < ∠ADC.
1 videos43 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
1 videos43 tests









