1. Name the obtuse angles found in the following diagram. We need to identify the angles whose measures are greater than 90º. Two angles are marked as right angles with ⌉ and ⌈ signs. We can get obtuse angles by annexing adjacent acute angles to these are angles.
m ∠TQR = m ∠TQP = 90º. Marked as right angles in the figure.
m ∠UQR = m ∠UQT + m ∠TQR Angle addition Property.
= measure of an acute angle + measure of a right angle > 90º.
Similarly,
m ∠PQS = m ∠PQT + m ∠TQS Angle addition Property
= measure of a right angle + measure of an acute angle > 90º.
Hence the two obtuse angles present in the given diagram are, angles UQR and PQS.
In the adjoining diagram, the measures of two vertical angles are given as linear expressions. Using the fact that vertical angles are congruent,
 Find the value of x
2. Determine whether the two angles vertical angles marked are obtuse.


We can equate the two linear expressions and solve for x.
7x + 2 = 6x + 15 Vertical angle are congruent. Hence their measures are equal.
 2  2

7x = 6x + 13
6x 6x

x = 13

Substituting x = 13 in one of the equations,
7x + 2 = 7(13) + 2 = 91 + 2 + 93º. The angle measure is greater than 90º.
Hence the two vertical angles marked are obtuse angles.Obtuse angle in Polygons:A triangle can have at most one obtuse angle. If a triangle has an obtuse angle then it is called an obtuse angled triangle.
In triangle ABC, measure of angle A is marked as 130º. Thus ABC is an obtuse angled triangle.
Oblique parallelograms have one pair of opposite angles obtuse. In general if two lines intersect, they form one pair of equal vertical angles obtuse, if they do not cut each other at right angles.