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
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
Prove that each angle of an equilateral triangle is 60°.
ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
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.
Fill the blank in the following so that the following statement is true.
Sides opposite to equal angles of a triangle are ......
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three altitudes.
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
Which of the following correctly describes the given triangle?
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
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 ______.
In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? 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.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
