Question

How many unique triangles can be made where one angle measures 60° and another angle is an obtuse angle?

Answer 1

Answer:

15 unique triangles can be made.      

Step-by-step explanation:

Given : A triangle has one angle measures 60° and another angle is an obtuse angle .

To find : How many unique triangles can be made ?

Solution : Since we know, that sum of all three angle of a triangle is 180°

One angle is 60°,

Second angle is obtuse angle(means angle is greater than 90°) then the third angle is acute angle(means less than 90°) .

$60^\circ+O+A=180^\circ$          

$O+A=120^\circ$  

$90^\circ+A+A=120^\circ$  

$A+A=30^\circ$  

This means the third angle is sum of two acute angle is 30°

So, The possible sum is (1+29),(2+28),(3+27),........(15+15)

Therefore, The possible ways the triangle can form is 15 ways.

Hence, 15 unique triangles can be made.                        

Answer 2

More than 2 unique triangles can be made where on angle measure 60 degrees and another angle is obtuse