Download (i) Angle - Mathguru

Q1.
Q2.
Q3.
Define the following terms:
(i) Angle (ii) Obtuse angle (iii) Complementary angles (iv)Supplementary angles
(v) Adjacent angles
Define and draw the following: (i) Linear pair of angles (ii) Vertically opposite
angles.
Find the complement of the following angles:
(i)
(ii)
Q4.
Find the supplement of the following angles:
(i)
(ii)
Q5.
Two supplementary angles are in the ratio
Q6.
In the given figure, lines
. Find the angles.
intersect at
. Find the measures of
.
Q7.
In the given figure
(i) Determine
when
(ii) Determine
when
intersect at
.
Q8.
In the given figure, what value of
Q9.
One of the four angles formed by two intersecting lines is a right angle. Show that
the other three angles will also be right angles.
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will make
, a straight line?
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Q10.
Fill in the blanks to make the following statements true:
(i) If two parallel lines are intersected by a transversal, then each pair of
corresponding angles are ……
(ii) Two lines parallel to the same line are …. each other.
(iii) If a transversal intersects two lines in such a way that the sum of interior
angles on the same side of the transversal is
then the lines are………..
Q11.
Q12.
Prove that the two lines which are both parallel to the same line are parallel to one
another.
In the given figure,
. Is
? Give two reasons.
Q13.
In the figure,
Q14.
In the figure,
Q15.
Two parallel lines are cut by a transversal such that one of the interior angles is
. Find each of the interior angles.
Q16.
In the given figure,
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. Find
.
, find
Find the value of
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Q17.
In the given figure,
, find the value of .
Q18.
In the given figure, prove that
Q19.
The sides
of a
.
have been produced to
, find all the angles of
Q20.
In
,
and
respectively. If
.
. Find the measure of
.
Answers
A1.
(i) An angle is formed when two rays originate from the same end point.
(ii) An angle whose measure is more than
but less than
is called an
obtuse angle.
(iii) Two angles are said to be complementary, if the sum of their measure is
.
(iv) Two angles are said to be supplementary, if the sum of their measure is
.
(v) two angles are called adjacent angles, if they have a common vertex, a
common arm and their non- common arms are on either side of the common arm.
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A2.
(i) Two adjacent angles are said to form a linear pair of angles, if their non –
common arms are two opposite rays.
from a linear pair of angles.
Sum of linear pair of angles is
.
(ii) Two angles are called a pair of vertically opposite angles, if their arms from two
pairs of opposite rays.
are two pairs of vertically
opposite angles. Vertically opposite angles are equal.
A3.
(i)
(ii)
A4.
(i)
(ii)
A5.
,
A6.
A7.
(i)
(ii)
A8.
A9.
A10.
A11.
A12.
Hint: Apply linear pair property and vertically opposite angles equal property.
(i) equal (ii) parallel (iii) parallel
Hint: Draw a transversal cutting the three lines, and then use the corresponding
angles axiom.
No, because alternate angles are not equal, interior angles on the same side of the
transversal are not supplementary.
A13.
A14.
A15.
A16.
A17.
A18.
A19.
Use exterior angle property and corresponding angles property.
A20.
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