Mathematics

In the figure given above, if $$ AC= AD= CD= BD $$; then $$\angle ABC $$ is $$ 30.5^{\circ} $$
If true then enter $$1$$ and if false then enter $$0$$


ANSWER

1


SOLUTION
In $$\triangle$$ ACD,
Since, AC = CD
$$\angle CAD = \angle CDA = x$$ (Angles opposite to equal sides are equal)
Sum of angles of the triangle,
$$\angle ACD + \angle CAD + \angle CDA = 180 $$
$$58 + 2x = 180$$
$$2x = 122$$
$$x = 61$$
In $$\triangle ABD$$,
AD = BD thus, $$\angle ABD = \angle DAB = y$$
Also, $$\angle ABD + \angle DAB = \angle ADC $$ (Exterior angle is equal to sum of opposite interior angles)
$$2\angle ABD = 61$$
$$\angle ABD = 30.5^{\circ}$$
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!


One Word 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
Find the measure of the complementary angle of each of $$20^o$$
  • A. $$50^o$$
  • B. $$160^o$$
  • C. $$80^o$$
  • D. $$70^o$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Subjective Medium
In the below figure $$AB,CD$$ and $$EF$$ are three lines concurrent at $$O$$. Find the value of $$y$$.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 Single Correct Medium
The angle that is three times as large as its complement is
  • A. $$135^o$$
  • B. $$50.5^o$$
  • C. $$45^o$$
  • D. $$67.5^o$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 One Word Medium
One angle of linear pair is a right angle, then find the measure of another angle.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Single Correct Medium
In figure, sides QP and RQ of $$\Delta PQR$$ are produced to points S and T respectively. If $$\angle SPR=135^o$$ and $$\angle PQT=110^o$$, find $$\angle PRQ$$.
  • A. $$85^o$$
  • B. $$45^o$$
  • C. $$35^o$$
  • D. $$65^o$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer