Mathematics

# Two lines $AB$ and $CD$ intersect at $O$. If $\angle AOC={50}^{o}$, find $\angle AOD, \angle BOD$ and $\angle BOC$

##### SOLUTION
From the figure we know that $\angle AOC$ and$\angle AOD$ from a linear pair

It can also be written as

$\angle AOC+\angle AOD={ 180 }^{ o }$

By substituting the values

${50}^{o}+\angle AOD={ 180 }^{ o }$

$\angle AOD={ 180 }^{ o }-{50}^{o}$

$\angle AOD={130}^{o}$

According to the figure we know that $\angle AOD$ and $\angle BOC$ are vertically opposite angles

So we get

$\angle AOD=\angle BOC={ 180 }^{ o }$

According to the figure we know that $\angle AOC$ and $\angle BOD$ are vertically opposite angles

So we get

$\angle AOC+\angle BOD={50}^{o}$

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
Which statement is not true?
• A. $\angle DOB$ is acute
• B. $\angle COE$ is a right angle
• C. $\angle AOE$ and $\angle BOE$ are supplementary angles.
• D. $\angle AOC$ and $\angle COE$ are complementary angles.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Subjective Medium
Two supplementary angles differ by $22 ^ { 0 }$. Find the angles.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Subjective Medium
In fig, if lines PQ and RS intersect at a point T such that $\angle PRT = 40 ^\circ$,$\angle RPT = 95 ^\circ$ and $\angle TSQ = 75 ^\circ$, find $\angle SQT$.

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q4 Single Correct Medium
If the angles of a triangle are in the ratio 2:3:4, find the three angles.
• A. $80^o, 120^o, 160^o$
• B. $20^o, 30^o, 40^o$
• C. None of these
• D. $40^o, 60^o, 80^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
Read the following two statements which are taken as axioms:
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^0$.