A triangle that contains an obtuse angle is called an obtuse triangle. It is also called as an obtuse angled triangle.
Due to the arrangement of three line segments as a closed geometric shape, three interior angles are formed inside a triangle.
In some cases, one of the three interior angles in a triangle can be an obtuse angle. Hence, the triangle can be called an obtuse triangle. It is also called an obtuse angled triangle.
In an obtuse triangle, one interior angle is an obtuse angle and remaining two interior angles are acute angles.
Geometrically, an obtuse triangle can be constructed by using geometric tools. So, let’s construct it firstly and then focus on studying its geometric properties practically.
Thus, a triangle, denoted by $QPR$ is constructed geometrically. In this example, the triangle $QPR$ contains an obtuse angle. Therefore, the triangle $QPR$ is called an obtuse triangle.
The $\Delta QPR$ contains three interior angles, and they are written as $\angle QPR$, $\angle PQR$ and $\angle QRP$.
The angle $QPR$ is known and it is $105^°$. Therefore $\angle QPR \,=\, 105^°$
For studying the obtuse angled triangle, we have to measure the remaining angles and it can be done by a protractor.
It is measured that
$(1).\,\,\,$ $\angle PQR \,=\, 34^°$
$(2).\,\,\,$ $\angle QRP \,=\, 41^°$
We can observe that the two angles are acute angles. Therefore, it is cleared that in an obtuse triangle, one angle is an obtuse angle and the remaining two angles are acute angles.
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