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
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
Find the measure of each exterior angle of an equilateral triangle.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
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.
Prove that each angle of an equilateral triangle is 60°.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
Write the sum of the angles of an obtuse triangle.
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
In the given figure, if AB ⊥ BC. then x =
In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
