Advertisements
Advertisements
Question
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?
Options
25°
30°
45°
60°
Advertisements
Solution
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
RELATED QUESTIONS
Show that the angles of an equilateral triangle are 60° each.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
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 triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
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.
Which of the following statements are true (T) and which are false (F):
The bisectors of two equal angles of a triangle are equal
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
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.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, the value of x is ______.
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
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.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
