Download App

Maths 5 Marks Questions

Properties of Parallel Lines · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 8 questions.

Questions

5 Marks Questions

Take a timed test

8 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks
In the given figure $\text{l || m}$ and t is a transversa. If $\angle1\ \text{and}\ \angle2$ are in the ratio $5 : 7$ find the measure of each of the angles $\angle1,\ \angle2,\ \angle3\ \text{and}\ \angle8.$
Answer


Given: $\text{l || m}$ t is a transversal.
$\angle1\ :\ \angle2\ =\ 5 : 7$
Let the angles measure $5x$ and $7x$
$\angle1+ \angle2=108^\circ$ (linear pair)
$\therefore\ 5\text{x}+7\text{x}=108^\circ$
$12\text{x}=180$
$ \text{x}=15$
$\therefore\ \angle1=5\text{x}=5(15)=75^\circ$
$\text{and}\ \angle2=7\text{x}=7(15)=105^\circ$
$\angle2+\angle3=180^\circ$ (linear pair)
$\angle3=180-105=75^\circ$
$\angle3+\angle6=180$ (interior angles on the same side of the transversal are supplementary)
$\angle6=180-\angle3=105^\circ$ and $\angle6=\angle8=105^\circ$ (vertically opposite angles)
$\therefore\ \angle1=75^\circ$
$\angle2=105^\circ$
$\angle3=75^\circ$
$\angle8=105^\circ$
View full question & answer→
Question 25 Marks
In the given figure, $AB || CD, \angle\text{ABE}=120^\circ,\ \angle\text{ECD}=100^\circ$ and $\angle\text{BEC}=\text{x}^\circ.$ Find the value of $x.$
Answer


Given: $AB || CD$
$\angle\text{ABE}=120^\circ$
$\angle\text{ECD}=100^\circ$
$\angle\text{BEC}=\text{X}^\circ$
Construction: $FEG || AB$
Now, sin ce $AB || FEG$ and $AB || CD, FEG || CD$
$\therefore\ \text{EFG || AB || CD}$
$\angle\text{ABE}=\angle\text{BEG}=120^\circ$ (alternate angles)
$\text{x}^\circ+\text{y}^\circ=120^\circ\ ....\text{(i)}$
$\angle\text{DCE}=\angle\text{CEF}=100^\circ$ (alternate angles)
$\text{x}^\circ+\text{z}^\circ=100^\circ\ ....\text{(ii)}$
Also, $\text{x}^\circ+\text{y}^\circ+\text{z}^\circ=180^\circ (FEG$ is a s traight line$) ....(iii)$
$2\text{x}^\circ+\text{y}^\circ+\text{z}^\circ=220^\circ$
$\text{x}^\circ+108^\circ=220^\circ ($substituting $(iii))$
$\therefore\ \text{x}^\circ=40$
$\therefore\ \text{x}=40$
View full question & answer→
Question 35 Marks
In the given figure $\text{l}\ ||\ \text{m}$ and t is a transversal. If $\angle5=70^\circ$ find the measure of each of the angles $\angle1,\ \angle3,\ \angle4\ \text{and}\ \angle8.$
Answer
Given: $\text{l}\ ||\ \text{m}$ t is a transversal.

$\angle5=70^\circ$
$\angle5=\angle3=70^\circ$ (alternate interior angles)
$\angle5+\angle8=180^\circ$ (linear pair)
$70^\circ+\angle8=180^\circ$
$\angle8=110^\circ$
$\angle1+\angle3=70^\circ$ (vertically opposite angles)
$\angle3+\angle4=180^\circ$ (linear pair)  
$\angle4=180-\angle3=180-70=110^\circ$
View full question & answer→
Question 45 Marks
In the given figure, $\text{l || m}$ and $\text{p || q}$ Find the measure of each of the angles $\angle\text{a},\angle\text{b},\angle\text{c}\ \text{and}\ \angle\text{d}.$
Answer


Given: $\text{l || m}$
$\text{p || q}$
$\angle1=65^\circ$
$\therefore\ \angle1=\angle\text{a}=65^\circ$ (vertically opposite angles)
$\angle\text{a}+\angle\text{d}=180^\circ$ (consecutive interior angles on the same side of a transversal are supplementary)
$\angle\text{d}=180^\circ-65^\circ=115^\circ$
$\angle\text{c}+\angle\text{d}=180^\circ$ (consecutive interior angles on the same side of a transversal are supplementary)
$\angle\text{c}=180^\circ-115^\circ=65^\circ$
$\angle\text{c}+\angle\text{b}=180^\circ$ (consecutive interior angles on the same side of a transversal are supplementary)
$\angle\text{b}=180^\circ-65^\circ=115^\circ$
$\therefore\ \angle\text{a}=65^\circ$
$\angle\text{b}=115^\circ$
$\angle\text{c}=65^\circ$
$\angle\text{d}=115^\circ$
View full question & answer→
Question 55 Marks
Two parallel lines $l$ and $m$ are cut by a transversal $t.$ If the interior angles of the same side of t be $(2x - 8)o$ and $(3x - 7)o,$ find the measure of each of these angles.
Answer


Given: $\text{l || m}$ t is a transversal.
Let: $\angle1=(2\text{x}-8)^\circ$
$\angle2=(3\text{x}-7)^\circ$
We know that the consecutive interior angles are supplementary.
$\therefore\ \angle1+\angle2=108^\circ$
$(2\text{x}-8)+(3\text{x}-7)=180$
$5\text{x}-15=180$
$5\text{x}= 195$
$\text{x} = 39$
$\angle1=(2\text{x}-8)=(2\times39-8)=70^\circ$
$\angle2=(3\text{x}-7)=(3\times39-7)=110^\circ$
View full question & answer→
Question 65 Marks
In the adjoining figure, it is given that $\text{CE || BA},\ \angle\text{BAC}=80^\circ$ and $\angle\text{ECD}=35^\circ.$ Find
$1. \angle\text{ACF},$
$2. \angle\text{ACB},$
$3. \angle\text{ACF}.$

Answer

From the question,
$CE \| BA , \angle BAC =80^{\circ}, \angle ECD =35^{\circ} \text {. }$
Now
$(i). \angle BAC =\angle ACE =80^{\circ}... [ \because$ Alternate angles $]$
$(ii).  \angle A C B,$
$ \Rightarrow \angle A C B+\angle A C D=180^{\circ}$
$ \Rightarrow \angle A C B+\angle A C E+\angle E C D=180^{\circ}$
$ \Rightarrow \angle A C B+80^{\circ}+35^{\circ}=180^{\circ}$
$ \Rightarrow \angle A C B+115^{\circ}=180^{\circ}$
$ \Rightarrow \angle A C B=180^{\circ}-115^{\circ}$
$ \Rightarrow \angle A C B=65^{\circ}$
$(iii). \angle A B C$
Let us consider $\triangle ABC$,
$ \angle ABC +\angle ACB +\angle BAC =180^{\circ}$
$ \Rightarrow \angle ABC +65^{\circ}+80^{\circ}=180^{\circ}$
$ \Rightarrow \angle ABC +145^{\circ}=180^{\circ}$
$ \Rightarrow \angle ABC =180^{\circ}-145^{\circ}$
$ \Rightarrow \angle ABC =35^{\circ}$
View full question & answer→
Question 75 Marks
In the given figure $\text{l || m}.$ If s and t be transversals such that s is not parallel to $t.$ find the values of $x$ and $y.$
Answer
From the given figure:

$\angle1=\angle3=50^\circ$ (corresponding angles)
and $\angle1=\text{x}^\circ=180^\circ$ (linear pair)
$\text{x}^\circ=180^\circ-50^\circ=130^\circ$
$\text{x}=130$
$\angle2=\angle4=65^\circ$ (corresponding angles) and $\angle2=\text{y}^\circ=180^\circ$ (linear pair)
$\text{y}^\circ=180^\circ-65^\circ=115^\circ$
$\text{y}=115$
View full question & answer→
Question 85 Marks
In the given figrue, $AB || CD$ and $CA$ has been produced to $E$ so that $\angle\text{BAE}=125^\circ.$ 
If $\angle\text{BAC}=\text{x}^\circ, \angle\text{ABD}=\text{x}^\circ,\angle\text{BDC}=\text{y}^\circ,$ and $\angle\text{ACD}=\text{z}^\circ,$ find the values of $x, y, z.$
Answer


Given: $AB || CD$
$\angle\text{BAE}=125^\circ$
$\angle\text{CAB}+\angle\text{BAE}=180^\circ$
$125^\circ + x^\circ = 180^\circ​​​​​​$
$x = 55 x + z = 180^\circ ($consecutive interior angles on the same side of transversal are supplementary$)$
$z = 180 - x$
$  = 180 - 55$
$  = 125 y + x = 180^\circ($consecutive interior angles on the same side of transversal are supplementary$)$
$y = 180 - x$
$   = 180 - 55$
$   = 125$
View full question & answer→
Generate Paper FreeAll Properties of Parallel Lines topics