we know that
The triangle is acute if the larger angle is less than [tex]90[/tex] degrees
The triangle is right if the larger angle is equal to [tex]90[/tex] degrees
The triangle is obtuse if the larger angle is greater than [tex]90[/tex] degrees
Remember that
The sum of the internal angles of a triangle is equal to [tex]180[/tex] degrees
so
In this problem
[tex]x+2x+3x=180\°[/tex]
Solve for x
[tex]6x=180\°[/tex]
[tex]x=30\°[/tex]
The angles of the triangle are
[tex]30\°-60\°-90\°[/tex]
The larger angle is equal to [tex]90[/tex] degrees
therefore
the answer is
right
Answer:
Right.
Step-by-step explanation:
According to the types of angles there are three types of triangle,
1) Acute triangle : a triangle with three acute angles (less than 90°)
2) Obtuse triangle : a triangle which having one obtuse angle (greater than 90°) and two acute angles.
3) Right triangle : a triangle which having one right angle and two acute angles.
Given,
The measures of the angles in a triangle are x, 2x, and 3x.
We know that the sum of all 3 interior angles of a triangle is supplementary,
⇒ x + 2x + 3x = 180° ⇒ 6x = 180° ⇒ x = 30°,
Hence, the measurement of the angles in the given triangle are,
30°, (2×30)°, (3×30)°
= 30°, 60°, 90°
Thus, by the above definitions,
Given triangle is right.
