Answer:
[tex] \fbox{A triangle can have 2 acute angles.}[/tex]
Step-by-step explanation:
Acute angle : The angle whose measure is less than 90° is called actute angle.
Obtuse angle : The angle whose measure is more than 90° is called obtuse angle.
Right angle : The angle whose measure is exact 90° is called right angle.
Property of triangle: The measure of all three angles of a triangle is 180°.
let's solve the actual question now,
Option A - let a triangle have two acute angle x and y respectively and z third angle of the respective triangle,
x + y + z = 180°
(<90°) + (<90°) + z = 180°
z = 180 - (<180)
z <180
the measure of 3rd angle z will be less than 180,
hence a triangle can have 2 acute angles.
Option B - let a right angle triangle have two right angles x and y respectively and z third angle of the respective triangle,
x+y+z = 180
90+90+z = 180
z = 180-180 = 0°
which means the third angle z does not exist and it is not a triangle. Hence a right angle triangle can only have one right angle.
Option C - let a triangle have two obtuse angle x and y respectively and z third angle of the respective triangle,
x + y + z = 180°
(>90°) + (>90°) + z = 180°
z = 180 - (>180)
when one number is subtracted from another number which is greater than that then the result obtain is negative. So the value of third angle z will be negative which is a flaw. Hence third option is also incorrect.
Option D - let a triangle have one right angle and one obtuse angle x and y respectively and z third angle of the respective triangle,
x + y + z = 180°
(90°) + (>90°) + z = 180°
z = 180 - (>180)
Same as option C, the third angle is negative which is a flaw and this option is incorrect too.
Conclusion- A triangle can have 2 acute angles and one right angle. So option A is the correct match.
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