How many triangles exist with the given angle measures 55,45,90 degrees A.Exactly one unique triangle exists with the given angle measures.

B .No triangle exists with the given angle measures.

C. More than one unique triangle exists with the given angle measures.

No triangle exists with the given angle measures ( 55° , 45° and 90° )

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

And , the measure of ∠ABC = 90°

Now , the measure of ∠BAC = 55°

And , the measure of ∠ACB = 45°

For the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

And , 90° + 55° + 45° = 190°

Therefore , the triangle is not possible

Hence , there is no triangle with measures ( 55° , 45° and 90° )

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Answer: The correct answer is B.

The first thing to check is the sum of the angles. 32 + 51 + 97 = 180. Therefore, the sides equal 180 and we can have a triangle because all triangles have exactly 180 degrees.

Second, the number of triangles with these measures is endless. Imagine taking the initial triangle and doubling the size. The angles don't change but the triangle does. We could keep doubling the size forever.