Mathematics

# In figure, lines $PQ$ and $ST$ intersect at $O$. If $\angle POR=90^o$ and $x:y =3:2$, then $z$ is equal to

##### ANSWER

$144^o$

##### SOLUTION
We can see in the given figure, $PQ$ is a straight line
$\therefore \angle POR +ROT +\angle TOQ =180^o$
$\Rightarrow 90^o +x+y=180^o$
$\Rightarrow x+y=90^o$
$\Rightarrow x+y=90^o$     ...(1)
Given that, $\dfrac xy =\dfrac 32$
Let $x=3K$ and $y=2K$
From equation (1)
$\Rightarrow 3K+2K=90^o$
$\Rightarrow K=\dfrac{90^o}{5}$
$\Rightarrow K=18^o$
$\therefore y=2\times 18^o =36^o$
Now, $SOT$ is a straight line
$\Rightarrow z+y=180^o$
$\Rightarrow z+36^o =180^o$
$\Rightarrow z=180^o-36^o$
$\Rightarrow z=144^o$
Hence, Option $(B)$ is correct.

You're just one step away

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

Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 85

#### Realted Questions

Q1 Subjective Medium
In $\Delta$ PQR, seg PM is a median of $\Delta$PQR. Bisectors of $\angle$PMQ and $\angle$PMR intersect side PQ and PR at X and Y respectively. Show that $\Delta$ PQR is similar to $\Delta$ PXY.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Subjective Medium
In the adjoining figure,$AOB$ is a straight line. Find the value of $x$, if $\angle AOC =60^0$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
A pair of angles with a common vertex and common arm are called
• A. complementary
• B. supplementary
• C. none
• D. adjacent angles

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
The supplement of a right angles is always ________ angle.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
In the given figure, the two lines $AB$ and $CD$ intersect at a point $O$ such that $\angle BOC={125}^{o}$. Find the values of $x,y$ and $z$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020