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
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.
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
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 a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
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.
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 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.
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
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)?
If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
In the given figure, for which value of x is l1 || l2?
In the given figure, the value of x is ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
Find all the angles of an equilateral triangle.
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.
