### Line and Angles

Geometry is basically the study of different properties of point, line and plane.
• The three angles in a triangle always add up to 1800
• The three angles of an equilateral triangle are all equal to 600
• Two angles of an isosceles triangle are equal.
• One angle of a right-angled triangle is 900
• All angles of an acute-angled triangle are acute angles, thus smaller than 900
• One angle of an obtuse-angled triangle is obtuse, thus larger than 900 and smaller than 1800

### Angle:

An angle is formed by two rays originating from the same end point.
The rays making an angle are called the arms of the angle and the end-points are called the vertex of the angle.

Types of Angles:-
(i) Acute angle: - An angle whose measure lies between 0° and 90°, is called an acute angle.

(ii) Right angle: - An angle, whose measure is equal to 90°, is called a right angle.
(iii) Obtuse angle: - An angle, whose measure lies between 90° and 180°, is called an obtuse angle. 180 degrees > Obtuse angle > 90 degrees

(iv) Straight angle: - The measure of a straight angle is 180°.

(v) Reflex angle: - An angle which is greater than 180° and less than 360°, is called the reflex angle.
(vi) Complimentary angle: - Two angles, whose sum is 90°, are called complimentary angle.

(vii) Supplementary angle: - Two angles whose sum is 180º, are called supplementary angle.

(viii) Adjacent angle: - Two angles are adjacent, if they have a common vertex, common arm and their non-common arms are on different sides of the common arm.
In the above figure angle ABC and DBC are adjacent angle. Ray BC is their common arm and point B is their common vertex. Ray BA and BD are uncommon arm.
When the two angles are adjacent, then their sum is always equal to the angle formed by the non-common arm.
Thus, angle ABD = angle ABC + angle DBC

(ix) Linear pair of angles: - If the sum of two adjacent angles is 180º, then their non-common lines are in the same straight line and two adjacent angles form a linear pair of angles.

(x) Vertically opposite angles: - When two lines AB and CD intersect at a point O, the vertically opposite angles are formed.

Angle pairs formed by parallel lines cut by a transversal
When two parallel lines are given in a figure, there are two main areas: the interior and the exterior.

When two parallel lines are cut by a third line, the third line is called the transversal. In the example below, eight angles are formed when parallel lines m and n are cut by a transversal line, t.

There are several special pairs of angles formed from this figure. Some pairs have already been reviewed:

Vertical pairs:

• angle 1 and 4
• angle 2 and 3
• angle 5 and 8
• angle 6 and 7
Recall that all pairs of vertical angles are congruent.
Supplementary pairs:

• angle 1 and 2
• angle 2 and 4
• angle 3 and 4
• angle 1 and 3
• angle 5 and 6
• angle 6 and 8
• sngle 7 and 8
• angle 5 and 7
Recall that supplementary angles are angles whose angle measure adds up to 180°. All of these supplementary pairs are linear pairs. There are other supplementary pairs described in the shortcut later in this section. There are three other special pairs of angles. These pairs are congruent pairs.

Alternate interior angles
two angles in the interior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate interior angles are non-adjacent and congruent.

Alternate exterior angles
two angles in the exterior of the parallel lines, and on opposite (alternate) sides of the transversal. Alternate exterior angles are non-adjacent and congruent.

Corresponding angles
two angles, one in the interior and one in the exterior, that are on the same side of the transversal. Corresponding angles are non-adjacent and congruent.

### Spotting Error Quiz IV - With Explanation For SSC Exam 2015

Hello Readers, As you know that Spotting Error types question is an important part of competitive examinations and seldom any book provide you the detailed solution. So we have decided to provide you the previous year questions of  spotting error along with the Explanation . If you like it let us know, you can also ask for detailed solutions of questions that are bothering you. 1.     I found (a)/ the two first chapters of the book (b)/ particularly interesting. (c)/ No error (d) Answer    (b) Explanation : It should be   ‘the first two chapters’ . 2.     Bacon, the father of the English easy (a) / had a thirst (b) / of knowledge (c) / No error (d) Answer    (a) Explanation : The English means the citizen of England.   Article is not used before language

### English Error Spotting - Previous Year Questions of SSC CGL

Competition Zenith brings you a post on Error Spotting to boost your English for competitive exams. We are providing you the specifically chosen questions from previous year papers of SSC CGL with the best possible explanation in simplest of the language. Below are some questions with explanation: Questions 1. Have trust on(a)/God and everything(b) /will be right.(c) /(d) No error 2. The cattles (a) /are grazing (b) /in the fields.(c) /(d) No error 3. He is one of (a)/ the best novelists (b) /that has ever lived. Do you agree? (c)/no error (d) 4. On a rainy day (a) /I enjoy to watch TV (b) / with a hot cup of tea.(c ) /no error(d) 5. No sooner did (a)/I reach (b)/ Patna railway station than the train departed(c)/no error (d) 6. There is no agreement (a) / between you and I (b) /so we are free to go our way(c) /no error (d) 7. A variety of books (a) / is available in the market (b) / to help the students qualify the competitive examinations.(c) /no error 8.

### Easy way to understand Direct and Indirect speech rules

Introduction. There two ways to convey a message of a person, or the words spoken by a person to other person. 1.       Direct speech 2.       Indirect speech Suppose your friend whose name is Vipul tells you in College , “I will give you a pen”. You come to home and you want to tell your brother what your friend told you. There are two ways to tell him. Direct speech:   Vipul said, “I will give you a pen”. Indirect Speech:  Vipul said that he would give me a pen. In direct speech   the original words of person are narrated (no change is made) and are enclosed in quotation mark. While in indirect speech some changes are made in original words of the person because these words have been spoken in past so the tense will change accordingly and pronoun may also be changed accordingly. In indirect speech  the statement of the person is not enclosed in quotation marks, the word “ that ” may be used before the statement to show that it is indirect sp