Advertisements
Advertisements
प्रश्न
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
Advertisements
उत्तर
In the given problem, angles of ΔABC are in the ratio 2:1:3
We need to find the measure of the smallest angle.
Let,
∠A = 2x
∠B = x
∠C = 3x
According to the angle sum property of the triangle, in ΔABC, we get,
2x + 1x + 3x = 180°
6x = 180°
`x = (180°)/6`
x = 30°
Thus,
∠A - 2(30°) = 60
∠B = 1(30°) = 30
∠C = 3(30°) = 90°
Since, the measure of ∠Bis the smallest of all the three angles.
Therefore, the measure of the smallest angle is 30°.
APPEARS IN
संबंधित प्रश्न
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
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.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
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.
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
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.
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.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In the given figure, if AB ⊥ BC. then x =
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
In the given figure, if l1 || l2, the value of x is
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
In ∆PQR, if ∠R > ∠Q, then ______.
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
In a triangle ABC, D is the mid-point of side AC such that BD = `1/2` AC. Show that ∠ABC is a right angle.
