Question
In parallelogram $FIST,$ find $\angle\text{SFT},\angle\text{OST}\ \text{and}\ \angle\text{STO}.$
✓
Answer
Given, $\angle\text{FIS}=60^\circ$
Now, $\angle\text{FTS}=\angle\text{FIS}=60^\circ$
Now, FT is parallel to $IS$ and $TI$ is a transversal,
therefore, $\angle\text{FTO}=\angle\text{SIO}=25^\circ$
$\therefore\angle\text{STO}+\angle\text{FTS}+=\angle\text{FTO}=60^\circ-25^\circ=35^\circ$ Also, $=\angle\text{FOT}+\angle\text{SOT}=180^\circ$
$\Rightarrow110^\circ+\angle\text{SOT}=180^\circ$
$\Rightarrow\angle\text{SOT}=180^\circ-110^\circ=70^\circ$
$\text{In}\triangle\text{TOS},\ \angle\text{TSO}+\angle\text{OTS}+\angle\text{TOS}=180^\circ$
$\therefore\ \angle\text{OST},=180-(70^\circ+35^\circ)=75^\circ$
$\text{In}\triangle\text{FOT},\ \angle\text{FOT}+\angle\text{FTO}+\angle\text{OFT}=180^\circ$
$\Rightarrow\angle\text{SFT}= \angle\text{OFT}=180^\circ-(\angle\text{FOT}+\text{FTO})$
$=180^\circ-(110^\circ+25^\circ)=45^\circ.$
Now, $\angle\text{FTS}=\angle\text{FIS}=60^\circ$
Now, FT is parallel to $IS$ and $TI$ is a transversal,
therefore, $\angle\text{FTO}=\angle\text{SIO}=25^\circ$
$\therefore\angle\text{STO}+\angle\text{FTS}+=\angle\text{FTO}=60^\circ-25^\circ=35^\circ$ Also, $=\angle\text{FOT}+\angle\text{SOT}=180^\circ$
$\Rightarrow110^\circ+\angle\text{SOT}=180^\circ$
$\Rightarrow\angle\text{SOT}=180^\circ-110^\circ=70^\circ$
$\text{In}\triangle\text{TOS},\ \angle\text{TSO}+\angle\text{OTS}+\angle\text{TOS}=180^\circ$
$\therefore\ \angle\text{OST},=180-(70^\circ+35^\circ)=75^\circ$
$\text{In}\triangle\text{FOT},\ \angle\text{FOT}+\angle\text{FTO}+\angle\text{OFT}=180^\circ$
$\Rightarrow\angle\text{SFT}= \angle\text{OFT}=180^\circ-(\angle\text{FOT}+\text{FTO})$
$=180^\circ-(110^\circ+25^\circ)=45^\circ.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Solve:$16-a^6+4 a^3 b^3-4 b^6$
→The given table shows the crop production of a State in the year $2008$ and $2009$. Observe the table given below and answer the given questions.
$a.$ For which crop$(s)$ did the production decrease?
$b.$ Write the production of all the crops in $2009$ in their standard form.
$c.$ Assuming the same decrease in rice production each year as in $2009$, how many acres will be harvested in $2015? $Write in standard form.
→|
Crop
|
$2008$ Harvest $($Hectare$)$
|
Increase/ Decrease $($Hectare$)$ in $2009$
|
|
Bajra
|
$1.4 \times 10^3$
|
$-100$
|
|
Jowar
|
$1.7 \times 10^6$
|
$-440,000$
|
|
Rice
|
$3.7 \times 10^3$
|
$-100$
|
|
Wheat
|
$5.1 \times 10^5$
|
$+190,000$
|
$b.$ Write the production of all the crops in $2009$ in their standard form.
$c.$ Assuming the same decrease in rice production each year as in $2009$, how many acres will be harvested in $2015? $Write in standard form.
Divide $54$ into two parts such that one part is $\frac{2}{7}$ of the other.
→Add the following Egyptian numeral :
In a district, the number of branches of different banks is given below:
Draw a pie chart for this data.
→|
Bank
|
State Bank of India
|
Punjab
|
National Bank
|
Canara Bank
|
|
Number of Branches
|
$30$
|
$17$
|
$15$
|
$10$
|
The table shows the data collected for Dhruv’s walking on a road.
$a.$ Plot a line graph for the given data using a suitable scale.
$b.$ In what time periods did Dhruv make the most progress?
→|
time $($in minutes$)$
|
$0$
|
$5$
|
$10$
|
$15$
|
$20$
|
$25$
|
|
Distsnce $($in $km)$
|
$0$
|
$0.5$
|
$1$
|
$1.25$
|
$1.5$
|
$1.75$
|
$b.$ In what time periods did Dhruv make the most progress?
Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.
Find the solution of the equation $5(3+y)=20+y$.
→The dimensions of a rectangular field are $80\ m$ and $18\ m$. Find the length of its diagonal.
→A mason has made a concrete slap. He needs it to be rectangular. In what different ways can he make sure that it is a rectangular?