Lines and Angles - Class 7 - Mathematics
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Exercise 5.1 - Lines and Angles | NCERT | Mathematics | Class 7
Find the complement of each of the following angles:
(i) $20^ \circ$
(ii) $ 63^ \circ$
(iii) $57^ \circ$
The complement of an angle is defined as an angle which, when added to the given angle, results in $90^\circ$. To find the complement of an angle $ theta $, we simply subtract the angle from $90^\circ$:
Complement of $20^\circ$: $90^\circ - 20^\circ = 70^\circ$
Complement of $63^\circ$: $90^\circ - 63^\circ = 27^\circ$
Complement of $57^\circ$: $90^\circ - 57^\circ = 33^\circ$
Hence, the complements are $70^\circ$, $27^\circ$, and $33^\circ$ respectively.
Find the supplement of each of the following angles:
(i) $105^ \circ$
(ii) $87^ \circ$
(iii) $154^ \circ$
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Sign up nowIdentify which of the following pairs of angles are complementary and which are supplementary.
(i) $65^{\circ}, 115^{\circ}$
(ii) $63^{\circ}, 27^{\circ}$
(iii) $112^{\circ}, 68^{\circ}$
(iv) $130^{\circ}, 50^{\circ}$
(v) $45^{\circ}, 45^{\circ}$
(vi) $80^{\circ}, 10^{\circ}$
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Sign up nowFind the angle which is equal to its complement.
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Sign up nowFind the angle which is equal to its supplement.
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Sign up nowIn the given figure, $\angle 1$ and $\angle 2$ are supplementary angles.
If $\angle 1$ is decreased, what changes should take place in $\angle 2$ so that both the angles still remain supplementary.
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Sign up nowCan two angles be supplementary if both of them are:
(i) acute?
(ii) obtuse?
(iii) right?
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Sign up nowAn angle is greater than $45^{\circ}$. Is its complementary angle greater than $45^{\circ}$ or equal to $45^{\circ}$ or less than $45^{\circ}$?
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Sign up nowFill in the blanks:
(i) If two angles are complementary, then the sum of their measures is
(ii) If two angles are supplementary, then the sum of their measures is
(iii) If two adjacent angles are supplementary, they form a
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Sign up nowIn the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
(ii) Adjacent complementary angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair
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Sign up nowExercise 5.2 - Lines and Angles | NCERT | Mathematics | Class 7
State the property that is used in each of the following statements?
(i) If $a \| b$, then $\angle 1=\angle 5$.
(ii) If $\angle 4=\angle 6$, then $a \| b$.
(iii) If $\angle 4+\angle 5=180^{\circ}$, then $a \| b$.
The given statements pertain to properties involving parallel lines cut by a transversal. Here are the properties used in each statement:
(i) If $a \| b$, then $\angle 1 = \angle 5$. This statement uses the Alternate Interior Angles Theorem, which states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is equal.
(ii) If $\angle 4 = \angle 6 $, then $ a \| b $. This statement also uses the Alternate Interior Angles Theorem but in the converse way. It suggests that if two angles formed by a transversal with two lines are equal, and those angles are alternate interior angles, then the two lines are parallel.
(iii) If $ \angle 4 + \angle 5 = 180^{\circ} $, then $ a \| b $. This statement uses the Consecutive Interior Angles Theorem, specifically the converse of it. It suggests that if two angles (additionally known as consecutive or same side interior angles) on the same side of a transversal sum up to 180 degrees, then the lines cut by the transversal are parallel. This is also known as the supplementary interior angles condition for parallel lines.
In the adjoining figure, identify
(i) the pairs of corresponding angles.
(ii) the pairs of alternate interior angles.
(iii) the pairs of interior angles on the same side of the transversal.
(iv) the vertically opposite angles.
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Sign up nowIn the adjoining figure, $p \| q$. Find the unknown angles.
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Sign up nowFind the value of $x$ in each of the following figures if $l \| \mathrm{m}$.
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Sign up nowIn the given figure, the arms of two angles are parallel.
If $\angle \mathrm{ABC}=70^{\circ}$, then find
(i) $\angle \mathrm{DGC}$
(ii) $\angle \mathrm{DEF}$
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Sign up nowIn the given figures below, decide whether $l$ is parallel to $m$.
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Sign up nowExtra Questions - Lines and Angles | NCERT | Mathematics | Class 7
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Steps of Construction:
Draw line segment $AB = 7.6$ cm.
Construct a ray $AX$ originating from point $A$ making an acute angle with $AB$.
Draw another ray $BY$ starting from point $B$ parallel to $AX$ such that it makes the same acute angle with $AB$ as $AX$.
On ray $AX$, mark points $A1, A2, A3, A4$, and $A5$ such that $AA1 = A1A2 = A2A3 = A3A4 = A4A5$. On ray $BY$, mark points $B1, B2, \ldots, \text{to } B8$ ensuring $BB1 = B1B2 = \ldots = B7B8$.
Draw a line from $A5$ to $B8$. Let the line intersect $AB$ at point $C$. This point $C$ divides $AB$ in the ratio $5:8$, therefore, $AC:CB = 5:8$.
By measuring the segments, $AC$ and $CB$, you can confirm the division of the line segment $AB$ in the ratio $5:8$.
Find the value of $x$ in the following diagram given that the horizontal lines are parallel to each other.
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