Download Q1. Find the measure of an angle. If seven times its complement is

Q1.
Find the measure of an angle. If seven times its complement is
less than three
Q2.
times its supplement.
In the given figure,
, find the value
from a linear pair. If
of
Q3.
In the figure, ray
of
stands on a line
respectively. If
bisects
. Rays
are the angle bisectors
. Find
Q4.
The ray
is the ray opposite to
Q5.
In the figure three coplanar lines intersects in a common point, forming angles as
shown. If
, then find angles
.
Q6.
In the given figure,
. If
, show that
.
is a straight line, find the values of
.
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Q7.
Two lines
intersected a point
such that
Find all four angles.
Q8.
Two straight lines
bisects
Q9.
, find
. Arm
the measure of
Q10.
intersect each other at point
. If
and
.
is produced upto point
is the bisector of
. Find
.
In the given figure
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find the value of .
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Q11.
In the given figure, prove that
Q12.
Q13.
If the arms of one angle are respectively parallel to the arms of another angle,
show that the two angles are either equal or supplementary.
If
, find the value of .
Q14.
In the given figure, the bisector of
Q15.
In the given figure,
divides
.
meet at
in the ratio
. Find the
and
.
. Determine the
value of .
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Q16.
Q17.
Q18.
Q19.
Q20.
If the sides of a triangle are produced in order, prove that the sum of the exterior
angles so formed is equal to four right angles.
If one angle of a triangle is equal to the sum of other two angles, show that the
triangle is a right angled triangle.
Two angles of triangles are equal and the third angle is greater than each one of
them by
. Find all the angles.
If two straight lines are perpendicular to the same line, prove that they are parallel
to each other.
If two parallel lines are intersected by a transversal, prove that the bisectors of
the two pairs of interior angles enclose a rectangle.
Answers
A1.
A2.
A3.
A4.
A5.
Hint: Opposite rays form linear pair of angles.
A6.
A7.
A8.
A9.
A10.
A11.
A12.
A13.
Hint: Prove
and
(alternate angles and co-interior angles). Then
lines parallel to the same line are parallel to each other.
Hint: Consider three cases here, Case 1: When both pairs of arms are parallel in
same sense, Case2: When both pairs of arms are parallel in opposite sense,
Case3: When one air of arms are parallel in same sense and other pair parallel in
opposite sense. Use the Alternate interior angles property and corresponding
angles property.
A14.
A15.
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A16.
A17.
Hint: Produce the sides of the triangle to get the exterior angles, Apply exterior
angle property for each of the exterior angles. Add the three equations and apply
angle sum property to get the result.
Hint: Apply angle sum property to find one of the triangle as
.
A18.
A19.
A20.
Hint: Use the property that the sum of the interior
angles on the same side of the transversal is
.
Hint: Prove that the figure formed by the bisectors of the two pairs of interior
angle is a parallelogram, one of whose angles is
.
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