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Published on: 16/09/2019
Lines and Angles
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1.
The angles of a triangles are (x-40), (x-20)o and \((\frac{x}{2}-10)^o\), Find the value of x and then the angles of the triangle.
2.
In the given figure, AF||BE, \(AC\bot BE\) and AF bisects \(\angle GAD.\) If \(\angle GAD=70^o\), then find the measure of \(\angle ABC\ and\ \angle ADE \)

3.
In \(\triangle ABC, if\ \angle A=(2x-5^o),\angle B=(5x+5^o),\angle C=(3x+50^o)\), then find the value of x, \(\angle A, \angle B\ and\ \angle C.\)
4.
An exterior angle of a triangle is 110o and one of the interior opposite angles is 30o. Find the measure of another two angles of the triangle.
5.
If a transversal intersects two parallel lines, then the bisectors of any pair of alternate angles are parallel. prove it.
6.
In given figure BA||ED and BC||EF. Show that \(\angle ABC=\angle DEF.\)

7.
In the figure PQ||RS, CBD is a transverse and \(\angle BCQ=135\). Find \(\angle RBD\)

8.
In the figure find 'x'

9.
In the figure AB || CD if \(\angle ABR=45^{ 0 }\) and \(\angle ROD=105^{ 0 }\) then find \(\angle \) ODC

10.
In the given figure AB ||CD and EF is transversal cutting them at G and H respectively.If \(\angle EGB=35^{ 0 }\) and QP \(\bot \) then find \(\angle PQH\)

11.
find the angles of a triangle PQR if \(\angle p-\angle q=45^{ 0 }\) and \(\angle Q-\angle R=30^{ 0 }\)
12.
An exterior angle of a triangle is \(115^{ 0 }\) and one of the interior opposite angles is \(35^{ 0 }\).Find the other two angles of the triangle.
13.
In figure \(\angle \) DOB =\(87^{ 0 }\) and \(\angle \) COA =\(82^{ 0 }\) If \(\angle \)BOA \(35^{ 0 }\) and Find \(\angle \) COB and \(\angle \)COD

14.
If (3x-\(58^{ 0 }\)) and (x+\(38^{ 0 }\)) are supplementary angles,find x and the angles.
15.
Find the supplement of \(\frac { 4 }{ 3 } \) of right angle
1.
\((x+40)^0+(x-20)^o+\left(\frac{x}{2}-10\right)^o=180^o\)
\(\Rightarrow \frac{5x}{2}-70=180^o\)
\(\Rightarrow \frac{5x}{2}=250^o\)
x=100o
So, angles are 60o, 80o and 40o
2.
AF||BE
\(\angle GAF=\angle DAF=\frac{70^o}{2}=35^o\)(AF bisects \(\angle GAD)\)
\(\angle DAF=\angle ADB=35^o\) (Alternate angles)
\(\therefore \angle ADE=180^o-35^o=145^o\)(L.P.A)
ext \(\angle GAD=\angle ABC+\angle ADB\)
(Exterior angle is the sum of the two opposite interior angles)
\(\Rightarrow 70^o=\angle ABC+35^o\)
\(\therefore \angle ABC=35^o\)
3.
In \(\triangle ABC\)
\(\angle A+\angle B+\angle C=180^o\) (Angle Sum prop. of \(\triangle)\)
2x-5o+5x+5o+3x+50o=180o
10x=130o
x=13o
\(\angle A=2x-5^o=21^o\)
\(\angle B=5x+5^o=70^o\)
\(\angle C=3x-50^o=89^o\)
4.
Exterior angle= Sum of opposite two interior angle
other angle =180-110=70o
110=30+x
x=80o
5.

\(\angle BMN=\angle CNM(alternate \angle 's)\)
\(\frac{1}{2}\angle BMN=\frac{1}{2}\angle CNM\)
x=y
(But x and y are alternate angles)
MP || NQ
6.
Construction: Extend AB to meet EF in P.

\(\angle ABC=\angle APF\) ..(i) (Corresponding angles)
Now \(\angle DEF=\angle APF\)...(ii) (Corresponding angles)
From (i) and (i)
\(\angle ABC=\angle DEF\)
7.
\(\angle DBS=\angle BCQ=135\) [Corresponding angles]
\(\angle RBD=180^o-\angle DBS\)
=180o-135o=45o
8.
\(110^{ 0 }\)
9.
\(30^{ 0 }\)
10.
\(55^{ 0 }\)
11.
\(100^{ 0 },55^{ 0 },25^{ 0 }\)
12.
\(80^{ 0 }\),\(65^{ 0 }\)
13.
\(\angle \)COB=\(47^{ 0 }\) ,\(\angle \)COD=\(40^{ 0 }\)
14.
x=50, \(92^{ 0 }\) and \(88^{ 0 }\)
15.
\(\frac{4}{3}\) of a right angle=\(\frac{4}{3}\times90^o=120^o\)
(Sum of supplementary angles is 180o)
Supplement of 120o=180o-120o=60o
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