Mathematics

# Two lines $AB$ and $CD$ intersect each other at a point $O$ such that $\angle AOC:\angle AOD=5:7$. Find all the angles.

##### SOLUTION
Consider $\angle AOC$ as $5x$ and $\angle AOD$ as $7x$
from the figure we know that $\angle AOC$ and $\angle AOD$ for linear pair of angle

so it can be written as

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

by substituting the values

$5x+7x={ 180 }^{ o }$

$x=180/12$

$x={15}^{o}$

by susbtituting the value of $x$

$\angle AOC=5x$

so we get

$\angle AOC=5(15)={75}^{o}$

$\angle AOD=7x$

so we get

$\angle AOD=7(15)={105}^{o}$

from the figure we know that $\angle AOC$ and $\angle BOD$ are vertical angles

so we get

$\angle AOC=\angle BOD={75}^{o}$

from the figures we know that $\angle AOD$ and $\angle BOC$ are vertical angles

so we get

$\angle AOD=\angle BOC={105}^{o}$

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 One Word Hard
The length of the perpendicular from the origin to a line is $7$ and the line makes angle of $150^o$. Which positive direction of y-axis. Find the equation of line.

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q2 Single Correct Medium
Find the angle which measure twice of its supplement.
• A. $100$
• B. $110$
• C. $130$
• D. $120$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 One Word Medium
In a triangle $ABC$, the line joining the circumcentre to the incentre is parallel to $BC$, then evaluate $\cos { B } +\cos { C }$

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q4 Single Correct Medium
If the length of the perpendicular drawn from the origin t the line whose intercepts on the axes are a and b be p. then
• A. ${ a }^{ 2 }+{ b }^{ 2 }={ p }^{ 2 }$
• B. ${ a }^{ 2 }+{ b }^{ 2 }=\dfrac { 1 }{ { p }^{ 2 } }$
• C. $\dfrac { 1 }{ { a }^{ 2 } } +\dfrac { 1 }{ { b }^{ 2 } } =\dfrac { 2 }{ { p }^{ 2 } }$
• D. $\dfrac { 1 }{ { a }^{ 2 } } +\dfrac { 1 }{ { b }^{ 2 } } =\dfrac { 1 }{ { p }^{ 2 } }$

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q5 Single Correct Medium
The measure of $\displaystyle \angle AOB$ in the following figure is:
• A. $\displaystyle 90^{\circ}$
• B. $\displaystyle 224^{\circ}$
• C. $\displaystyle 134^{\circ}$
• D. $\displaystyle 44^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020