Advertisements
Advertisements
प्रश्न
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?
विकल्प
25°
30°
45°
60°
Advertisements
उत्तर
In the given figure, measures of the angles of ΔABC are in the ratio 3 : 4 : 5. We need to find the measure of the smallest angle of the triangle.
Let us take,
∠A = 3x
∠B = 4x
∠C = 5x
Now, applying angle sum property of the triangle in ΔABC, we get,
∠A + ∠B + ∠C = 180°
3x + 4x + 5x = 180°
12X = 180°
`x = (180°)/ 12`
x = 15°
Substituting the value of x in ,∠A,∠Band∠C
∠A = 3(15°) = 45
∠B = 4(15V) = 60
∠C = 5(15°) = 75°
Since, the measure of ∠A is the smallest
Thus, the measure of the smallest angle of the triangle is 45°
APPEARS IN
संबंधित प्रश्न
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
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.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
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.
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)
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)?
If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In the given figure, x + y =
In the given figure, what is the value of x?
In the given figure, if BP || CQ and AC = BC, then the measure of x is
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
Find all the angles of an equilateral triangle.
