Advertisements
Advertisements
प्रश्न
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
विकल्प
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
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Prove that the medians of an equilateral triangle are equal.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
The bisectors of two equal angles of a triangle are equal
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
Write the sum of the angles of an obtuse triangle.
If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
Which of the following correctly describes the given triangle?
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
