**Angle**

An angle is a combination of “two rays” (half lines) with a common end point.

**a.** Common end point = vertex

**b.** Rays as the sides = legs or arms of the angle.

**Acute angle**

Less than 90o

**a.** An angle whose measure is less than 90o is called an acute angle.

**b.** Acute angles are the smallest being between 0 and 90o.

**Obtuse angle**

Between 90o and 180o

An angle whose measure is greater than 90o but less than 180o, is called an obtuse angle.

**Right angle**

An angle whose measure is exactly 90o.

**Straight angle**

An angle whose measure is exactly 180o i.e. a straight line

**Reflex angle**

An angle whose measure is greater than 180 o but less than 360o is a reflex angle.

**Full angle**

An angle whose measure is exactly 3600 i.e. a full circle

**Allied angles**

**a.** “Allied angle is an angle pair, which is created by trans-versal line.”

**b.** Allied angles are also known as:

(i) Co-interior (ii) Adjacent interior

**Explanation**

**a.** If I draw two parallel lines cut by a transversal, then allied angles are between the parallel lines and on the same side of transversal.

**b.** The allied angle theorem states that allied angles are supplementary.

**c.** A line that meets two or more parallel lines is called a transversal line.

**5.** **Complementary angles**

**a.** Two angles whose sum totals 90o degree.

**b.** Two angles are complementary when they add up to 90o degrees.

**c.** They don’t have to be next to each other; just the sum total must be 90o.

**Example**

**(i)** 60o and 30o are complementary angles.

**(ii)** 5o and 85o are complementary angles.

**6.** Supplementary angles

Two angles are supplementary when they add up to 180o.

**Example**

**(i)** 60o and 120o are supplementary angles.

**(ii)** 93 and 87 are supplementary angles.

**7. Vertical angles**

Vertical angles are the angles opposite to each other when two lines cross. They are always equal.

**8.** **Triangle**

A triangle is a closed figure with three lines and three angles. These three angles always add up to 180o.

**9.** **Right angle triangle**

A triangle in which the measure of one angle equals 90o degree.

**10.** **Isosceles triangle**

An isosceles triangle has two equal sides. The angles opposite to equal sides are also equal.

**11.** **Right isosceles triangle**

A right triangle that has 2 sides and 2 angles equal.

**Explanation:**

**a.** In such a triangle, one angle is of 90o and other two are of 45o each.

**b.** This triangle satisfies the Pythagorean Theorem.

**12.** Scalene triangle

A triangle with all sides of different lengths and different angles is called a scalene triangle.

**13. Acute angle triangle**

A triangle in which measures of all angles are less than 90o.

**14. Obtuse triangle**

Obtuse triangle is the one in which the measure of one triangle is greater than 90o.

**15. Equilateral triangle**

A triangle having three equal sides and three equal angles of 60o is called an equilateral triangle.