Mathematics

Two lines $AB$ and $CD$ intersect at a point $O$ such that $\angle BOC+\angle AOD={280}^{o}$, as shown in the figure. Find all four angles.

SOLUTION
From the figure we know that $\angle AOD$ and $\angle BOC$ are vertically opposite angles $\angle AOD=\angle BOC$

It is given that

$\angle BOC+\angle AOC={ 280 }^{ o }$

we know that $\angle AOD=\angle BOC$

so it can be written as

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

$2\angle AOD={ 280 }^{ o }$

$\angle AOD=\dfrac{180}{2}$

$\angle AOD=\angle BOC={ 140 }^{ o }$

From the figure we know that $\angle AOC$ and $\angle AOC$ form a linear pair

So it can be written as

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

substituting the values

$\angle AOC+{ 140 }^{ o }={ 180 }^{ o }$

$\angle AOC={40}^{o}$

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

$\angle AOC=\angle BOD={40}^{o}$

Therefore $\angle AOC={40}^{o}$, $\angle BOC={ 140 }^{ o }$, $\angle AOD={ 140 }^{ o }$, $\angle BOD={ 40 }^{ o }$

You're just one step away

Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87

Realted Questions

Q1 Subjective Medium
From figure, write all pairs of parallel lines.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
An angle which measures $\displaystyle 180^{0}$ is called-
• A. Acute
• B. Right
• C. Zero
• D. None of these

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
$\begin{array} { l } { \text { In fig. find the values of } x \text { and } y \text { and then } } \\ { \text { Show that } A B \| C D } \end{array}$
• A. $x=100$ and $y=130$
• B. $x=230$ and $y=130$
• C. None of these
• D. $x=130$ and $y=130$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Single Correct Medium
Consider the following statements:
Two lines intersected by a transversal are parallel if:
1. the pairs of corresponding angles are equal.
2. the interior angles on the same side of the transversal are supplementary.
Which of the statements given above is/are correct?
• A. $1$ only
• B. $2$ only
• C. Neither $1$ nor $2$
• D. Both $1$ and $2$

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q5 Subjective Medium
If two angles have a common vertex and their arms form opposite rays Fig., Then, how many angles are formed?

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020