Math Problem Statement

एका त्रिकोणाचे तिन्ही कोनांचे गुणोत्तर 1:2:3 प्रमाणे आहे तर सर्वात लहान कोण किती अंशाचा असेल?

Solution

The given question is in Marathi, and it asks:

In a triangle, the three angles are in the ratio 1:2:3. What is the measure of the smallest angle?

Solution:

The sum of all angles in any triangle is always 180180^\circ. Let's assume the angles are xx, 2x2x, and 3x3x (since they are in the ratio 1:2:3).

So, the equation is: x+2x+3x=180x + 2x + 3x = 180^\circ 6x=1806x = 180^\circ x=1806=30x = \frac{180^\circ}{6} = 30^\circ

Thus, the smallest angle is 3030^\circ.

Correct Option:

The correct answer is C. 30

Would you like more details on the solution or any further clarifications? Here are 5 related questions for practice:

  1. If the angles of a triangle are in the ratio 2:3:5, what is the smallest angle?
  2. What is the largest angle in a triangle with angles in the ratio 1:4:5?
  3. If one angle of a triangle is 4545^\circ and the other two are in the ratio 3:4, what are the other two angles?
  4. In a right-angled triangle, if one of the angles is 3030^\circ, what is the other angle?
  5. Can a triangle have angles in the ratio 1:1:4?

Tip: Always remember that the sum of interior angles of any triangle is 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Ratio of angles in a triangle
Sum of angles in a triangle

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle angle sum theorem

Suitable Grade Level

Grade 7-8