Mathematics

In the figure, $$PQR$$ is a straight line. Find $$x$$. Then complete the following :
(i) $$\angle AQB=$$
(ii) $$\angle BQP=$$
(iii) $$\angle AQR=$$


SOLUTION
In the given fig., $$\angle{PQA}, \angle{AQB}$$ and $$\angle{BQR}$$ forms a linear pair.

Therefore,

$$\angle{PQA} + \angle{AQB} + \angle{BQR} = 180°$$

$$\left( x + 20° \right) + \left( 2x + 10° \right) + \left( x - 10° \right) = 180°$$

$$4x + 20° = 180°$$

$$\Rightarrow x = \cfrac{180° - 20°}{4} = 40°$$

Therefore,

$$\angle{AQB} = 2x + 10° = 2 \times 40° + 10° = 90°$$

$$\angle{BQP} = \left( x + 20° \right) + \left( 2x + 10° \right) = 3x + 30° = 3 \times 40° + 30° = 150°$$

$$\angle{AQR} = \left( 2x + 10° \right) + \left( x - 10° \right) = 3x = 3 \times 40° = 120°$$
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 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Can two angles be supplementary if both of them are: (i) acute (ii) obtuse (iii) right? 

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Subjective Medium
The measure of an angle is twice the measure of its supplementary angle. Find its measure.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 One Word Medium
If true then enter $$1$$ and if false then enter $$0$$
Can two obtuse angles be supplementary?

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Subjective Medium
In the given diagram, $$ABC$$ is a straight line
If $$x=53^o$$ find $$y$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Subjective Medium
Fill in the blanks:
If two lines intersect a point, then the vertically opposite angles are always ______.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer