Answer:
False
Step-by-step explanation:
We are given that a triangle in which two acute angles .
Then, the triangle must be a right triangle .
We have to find that it is true or false.
Acute angle: That angle whose measure is less than 90 degrees.
Right triangle : That triangle in which one angle measure is equal to 90 degrees.
Let x, y and z are angles of a triangle
Suppose, we have x=70 degrees , y= 60 degrees
Then , [tex]x+y+z=180^{\circ}[/tex] (triangle angles sum property)
[tex]70+60+z=180[/tex]
[tex]130+z=180[/tex]
[tex]z=180-130=50^{\circ}\neq 90^{\circ}[/tex]
Hence, the triangle must not be right triangle in that case.
When x=y=45 degrees
Then , [tex]45+45+z=180[/tex]
[tex]90+z=180[/tex]
[tex]z=180-90=90^{\circ}[/tex]
Hence, the triangle must be right triangle in that case.
Therefore, a triangle with acute angles must be right triangle is true when two acute angles measure are of 45 degrees each not in every case.
Hence, a triangle with two acute angles must not be a right triangle.
Answer: False
