Advertisements
Advertisements
प्रश्न
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
Advertisements
उत्तर
Consider a ΔABC,
Given that ∠A = 120° and AB = AC and given to find ∠B and ∠C
We can observe that DABC is an isosceles triangle since AB = AC
⇒∠B=∠C ………(1) [Angles opposite to equal sides are equal]
We know that sum of angles in a triangle is equal to `180^@`
`⇒∠A+∠B+∠C=180^@`
⇒`∠A+∠B+∠B=180^@` [from (1)]
⇒`120^@+2∠B=180^@`
⇒`2∠B=180^@-120^@`
⇒`2∠B=60^@⇒∠B=30^@`
⇒`∠C=∠B=30^@`
APPEARS IN
संबंधित प्रश्न
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
Find the measure of each exterior angle of an equilateral triangle.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
Find the measure of each exterior angle of an equilateral triangle.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
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.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles of a triangle are ......
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
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.
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
