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 $$\angle{ABD}=3\angle{DAB}=3\times {24}^{\circ}={72}^{\circ}$$
View Answers

You're just one step away

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


Subjective Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87
Enroll Now For FREE

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

View Answer
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

View Answer
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

View Answer
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

View Answer
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

View Answer