Mathematics

# If the sides of a triangle are produced, then the sum of the exterior angle i.e. $\angle a+\angle b+\angle c$ is equal to

${ 360 }^{ 0 }$

##### SOLUTION
In $\triangle ABC$,
$\angle a = \angle ABC + \angle ACB$ (Exterior angle property)
$\angle b = \angle ACB + \angle BAC$ (Exterior angle property)
$\angle C = \angle ABC + \angle BAC$ (Exterior angle property)

Adding all the equations:
$\angle a + \angle b + \angle c = 2 (\angle ABC + \angle ACB + \angle BAC)$
$\angle a + \angle b + \angle c = 2 (180)$
$\angle a + \angle b + \angle c = 360^{\circ}$

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!

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

#### Realted Questions

Q1 Single Correct Medium
In the given figure $l \parallel \overset {\leftrightarrow}{AB}$ and $l$ intersects $\overline {AC}$ and $\overline {BC}$ at $P$ and $Q$ respectively. If $CP = 3, PA = 4, QB = 6$ then $BC =$ ________.
• A. $12.5$
• B. $7.5$
• C. $4.5$
• D. $10.5$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
The line parallel to the x-axis and passing through the intersection of the lines ax+2by+3b=0 and bx-2ay-3a=0, where $(a,b)$
• A. Below the x-axis at a distance of $\dfrac { 3 }{ 2 }$
• B. Above the x-axis at a distance of $\frac { 3 }{ 2 }$ from it
• C. Above the x-axis at a distance of $\dfrac { 3 }{ 2 }$ from it
• D. Below the x-axis at a distance of $\dfrac { 3 }{ 2 }$ from it

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
If two supplementary angles are in the ratio $4:5$, then the angles are __________.
• A. $85^o, 95^o$
• B. $40^o, 50^o$
• C. $60^o, 120^o$
• D. $80^o, 100^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
Find x:

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
From the adjoining figure find $x$,  i $AOB$ is a straight line. Hence complete the following
Which is an acute angle?

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020