Lines and Angles

Q. In the $\Delta$ PQR, PS is the bisector of $\angle P$ and PT $\perp$ QR, then $\angle TPS$ is equal to

1. ${90}^{\circ }-\frac{1}{2}\angle R$
2. $\angle Q+\angle R$
3. ${90}^{\circ }+\frac{1}{2}\angle Q$
4. $\frac{1}{2}(\angle Q-\angle R)$

Q. Given that AB || CD and CE || FG determine $\angle EFG.$

1. ${150}^{\circ }$
2. Inadequate data
3. ${115}^{\circ }$
4. ${145}^{\circ }$

Q. Three straight lines, $X,YandZ$ are parallel and the angles are as shown in the figure below. What is $\angle AFB$ equal to?

1. ${20}^{\circ }$
2. ${10}^{\circ }$
3. ${15}^{\circ }$
4. ${30}^{\circ }$

Q. In the given figure, $l_1$ is parallel to $l_2$, AB and BC are angle bisectors. Find the measure of $\angle ABC$

1. 90
2. 60
3. 80
4. 70

Q. In the given figure, AB || CD and AC || BD. If $\angle EAC={40}^{\circ },\angle FDG={55}^{\circ },\angle HAB=x^{\circ },$ then find the value of x.

1. ${55}^{\circ }$
2. ${85}^{\circ }$
3. ${75}^{\circ }$
4. ${65}^{\circ }$

Q. Given that segment AB and CD are parallel, if lines l, m and n interesect at point O. Find the ratio of $\theta$ to $\angle ODS$.

1. 3 : 2
2. 2 : 3
3. Data insufficient
4. 3 : 4

Q. In the adjoining figure, ABCD is a rectangle and DF = CF also, AE = 3BE. What is the value of $\angle EOF,if\angle DFO={28}^{\circ }and\angle AEO={42}^{\circ }?$

1. ${14}^{\circ }$
2. ${42}^{\circ }$
3. ${70}^{\circ }$
4. ${90}^{\circ }$

Q. In a $\Delta ABC$, a line XY parallel to BC intersects AB at X and AC at Y:
If BY bisects $\angle XYC$, then $\angle CBY$ : $\angle CYB$ is:

1. 5 : 4
2. 4 : 5
3. 1 : 1
4. 6 : 5

Q. In the given figure, $PQ||ST,TV||RSandTU\perp ST.$ Find $\angle QRS.$

1. None of these
2. ${120}^{\circ }$
3. ${125}^{\circ }$
4. ${135}^{\circ }$

Q. In the given figure, AB || CD, $\angle ABO={40}^{\circ }$ and $\angle CDO={30}^{\circ }.$ If $\angle DOB=x,$ then find the value of x.

1. ${10}^{\circ }$
2. ${110}^{\circ }$
3. ${70}^{\circ }$
4. ${20}^{\circ }$