Mathematics

# In the adjoining figure, AB$||$CD and PQ, QR intersects AB and CD both at E, F and G, H respectively. Given that $\angle$PEB$=80^o$, $\angle$QHD$=120^o$ and $\angle$PQR$=x^o$, find the value of x.

$20$

##### SOLUTION
$\angle PEB=\angle PGD \,\,(\because AB||CD)$
$\therefore \angle PGD=80^o$
$\angle QGD=180-\angle PGD=180-80=100^o$
$\angle QHC=180-\angle QHD=180-120=60^o$
In $\triangle QGH:$
$x+\angle QGD+\angle QHC=180^o\\ \Rightarrow x=180-100-60=20^o$

You're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
If two straight lines intersect the measures of the vertically opposite angles are ____
• A. not equal
• B. cannot be determined
• C. none of these
• D. equal

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
The measure of an angle which is 5 times its supplement is
• A. $30^o$
• B. $60^o$
• C. $120^o$
• D. $150^o$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
Two complementary angles are in the ratio $1:9$. The angles are:
• A. $54^\circ,\, 36^\circ$
• B. $10^\circ,\, 90^\circ$
• C. $11^\circ,\, 79^\circ$
• D. $9^\circ,\, 81^\circ$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
In $\Delta PQR$ S is a point on PQ such that SR = QR = SP. and $\angle PSR=120^{\circ}$ .Find $\angle P$ .

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
What is an Obtuse Angle ?

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020