Mathematics

# In the figure, $\angle ABD=3 \angle DAB$ and $\angle BDC=96^{o}$, Find $\angle ABD$

##### SOLUTION
In $\triangle ABC$
$\angle{ABD}=3\angle{DAB}$ (given)
and $\angle{BDC}={96}^{\circ}$
$\angle{BDC}+\angle{BDA}={180}^{\circ}$ (linear pair)
$\Rightarrow {96}^{\circ}+\angle{BDA}={180}^{\circ}$
$\Rightarrow \angle{BDA}={180}^{\circ}-{96}^{\circ}={84}^{\circ}$
In $\triangle{ABD}, \angle{ABD}+\angle{DAB}+\angle{BDA}={180}^{\circ}$ (angle sum property)
$\Rightarrow 3\angle{DAB}+\angle{DAB}+{84}^{\circ}={180}^{\circ}$
$\Rightarrow 4\angle{DAB}={180}^{\circ}-{84}^{\circ}={96}^{\circ}$
$\Rightarrow \angle{DAB}=\dfrac{{96}^{\circ}}{4}={24}^{\circ}$
and $\angle{ABD}=3\angle{DAB}=3\times {24}^{\circ}={72}^{\circ}$

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
In the figure $\angle B$ is equal to
• A. $85^{\circ}$
• B. $70^{\circ}$
• C. $115^{\circ}$
• D. $95^{\circ}$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
The joint equation of the pair of lines through (3, 2) and parallel to the lines $x = 2$ & $y = 3$ is:
• A. $xy-3x-2y+6=0$
• B. $xy-3x-2y-6=0$
• C. $xy+3x+2y-6=0$
• D. $xy-2x-3y+6=0$

Asked in: Mathematics - Straight Lines

1 Verified Answer | Published on 17th 08, 2020

Q3 Single Correct Medium
The sum of all six exterior angles of triangle is ___________.
• A. $180$
• B. $360$
• C. $90$
• D. $720$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Single Correct Medium
If two supplementary angles are in the ratio $1:2$, then the bigger angle is
• A. $125^o$
• B. $110^o$
• C. $90^o$
• D. $120^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 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