Mathematics

# In the figure, $AOB$ is a straight line, Find the value of $x$. Hence, find $\angle AOC$ and $\angle BOD$.

##### SOLUTION
From the figure we know that $\angle AOB$ is a straight line

So we get

$\angle AOB={180}^{o}$

It can also be written as

$\angle AOC+\angle COD+\angle BOD={180}^{o}$

By substituting the values

${(3x-7)}^{o}+{55}^{o}+{(x+20)}^{o}={180}^{o}$

$3x-{7}^{o}+{55}^{o}+x+{20}^{o}={180}^{o}$

On further calculate

$4x+{180}^{o}={180}^{o}$

$4x={112}^{o}$

$x={28}^{o}$

By substituting the value of $x$ we get

$\angle AOC={(3x-7)}^{o}=3({28}^{o})-{7}^{o}$

$={84}^{o}-{7}^{o}={77}^{o}$

$\angle BOD={(x+20)}^{o}={(28+20)}^{o}={48}^{o}$

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 Single Correct Medium
An angle measuring $91^{o}$ is
• A. an acute angle
• B. an obtuse angle
• C. a reflex angle
• D. none of this

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
If two angles are complementary and in the ratio $17:13$. Find the measure of angles.
• A. $61^o, 29^o$
• B. $71^o, 19^o$
• C. $17^o, 13^o$
• D. $51^o, 39^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
The ratio between two complementary angles is $2 : 3$: find the smallest angle.
• A. $26$
• B. $25$
• C. $45$
• D. $36$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Single Correct Medium
Two supplementary angles are in ratio $4:5$. Find the measure of greater angle.
• A. $\displaystyle { 70 }^{ o }$
• B. $\displaystyle { 80 }^{ o }$
• C. $\displaystyle { 110 }^{ o }$
• D. $\displaystyle { 100 }^{ o }$

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 $180^0$.