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 ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
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)?
Sum of any two sides of a triangle is greater than the third side.
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.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
Fill in the blank to make the following statement true.
The sum of three altitudes of a triangle is ..... than its perimeter.
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.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, what is z in terms of x and y?
In the given figure, what is the value of x?
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
In ∆PQR, if ∠R > ∠Q, then ______.
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.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
