Question

A triangle has the following angle measures: 125°, 15°, and 40°. Which of the following statements best describes its drawing?

A)It is impossible to construct a triangle with these angle measures.
B)There is one possible triangle with these angle measures.
c)There are many possible triangles with these angle measures.
D)There are many possible similar triangles with these angle measures.

Answer 1

The answer should Be D

Answer 2

Answer: Option 'D' is correct.

Explanation:

Since we have given that

Measures of angles are as follows:

125°, 15°, 40°

As we know the sum of all angles in a triangle is supplementary i.e. 180°.

∠A+∠B+∠C=180°

125°+15°+40°=180°

Therefore, it is satisfying the angle sum property.

So, it can form a triangle.

Now, we will check for uniqueness.

As similar triangles need two angles to be equal by AA criteria , their sides can vary with two equal angles.

Hence, there is possibility to have many possible similar triangles with angle measures.

Therefore, Option 'D' is correct.