Determine the nature of the following triangles.
We know that:
\widehat{A}+\widehat{B}+\widehat{C} = 180^\circ
75^\circ + \widehat{B} + 30^\circ=180^\circ
Therefore:
\widehat{B} =75^\circ
The triangle has two congruent angles.
This triangle is isosceles.
We know that:
\widehat{A}+\widehat{B}+\widehat{C} = 180^\circ
\widehat{A} + 30^\circ + 60^\circ=180^\circ
Therefore:
\widehat{A} =90^\circ
This triangle is right-angled.
This triangle is right-angled.
The triangle is isosceles as it has two congruent sides. In particular,
\widehat{B} = \widehat{C}
We know that:
\widehat{A}+\widehat{B}+\widehat{C} = 180^\circ
60^\circ + \widehat{B} +\widehat{B} =180^\circ
60^\circ + 2\widehat{B} =180^\circ
2\widehat{B} =120^\circ
\widehat{B} =60^\circ
Therefore:
\widehat{A} = \widehat{B} = \widehat{C} = 60^\circ
This triangle is equilateral.
The triangle is isosceles as it has two congruent sides. In particular,
\widehat{B} = \widehat{C}
We know that:
\widehat{A}+\widehat{B}+\widehat{C} = 180^\circ
60^\circ + \widehat{B} +\widehat{B} =180^\circ
60^\circ + 2\widehat{B} =180^\circ
2\widehat{B} =120^\circ
\widehat{B} =60^\circ
Therefore:
\widehat{A} = \widehat{B} = \widehat{C} = 60^\circ
This triangle is equilateral.
Since the triangle has an obtuse angle, it is an obtuse triangle.
The triangle AOC is isosceles right triangle, hence we have
\widehat{C} = 45^\circ
The triangle AOB is isosceles right triangle, hence we have
\widehat{B} =45^\circ
We know that:
\widehat{A}+\widehat{B}+\widehat{C} = 180^\circ
\widehat{A} +45^\circ + 45^\circ =180^\circ
\widehat{A} =90^\circ
This is an isosceles right triangle.
We know that:
\widehat{A}+\widehat{B}+\widehat{C} = 180^\circ
80^\circ + 55^\circ +\widehat{C} =180^\circ\\135^\circ +\widehat{C} =180^\circ\\\widehat{C} =45^\circ
The triangle has three angles of different measures.
This triangle is scalene.