Advertisements
Advertisements
प्रश्न
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
पर्याय
60°
120°
150°
30°
Advertisements
उत्तर
In the given ΔABC,∠A = 60° and ∠B = 80° . Bisectors of ∠B and ∠C meet at O.
We need to find ∠BOC
Since, OB is the bisector of ∠B.
Thus, `∠OBC = 1/2 ∠ABC ..... (1)`
Now, using the angle sum property of the triangle
In ΔABC, we get,
∠A + ∠B + ∠C =180°
60° + 80° + ∠C = 180°
140° + ∠C = 180°
∠C = 180° - 140°
∠C = 40°
Similarly, in ΔBOC
∠OBC + ∠O + ∠OCB = 180
∠O + 20° + 40°=180°
∠O + 60° = 180°
∠O = 180° - 60°
= 120°
Hence, ∠BOC = 120°
APPEARS IN
संबंधित प्रश्न
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
Write the sum of the angles of an obtuse triangle.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, for which value of x is l1 || l2?
In the given figure, what is y in terms of x?
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
Find all the angles of an equilateral triangle.
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
