7th Grade > Mathematics
LINES AND ANGLES MCQs
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Given - the complementary angles are equal.
Let the angle be x. So its complement = x.
⇒x+x=90∘
⇒2x=90∘
⇒x=45∘
The angle which is complementary to itself is x=45∘.
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Steps: 1 Mark
Answer: 1 Mark
The angles of a right-angled isosceles triangle are:
90∘, 45∘ and 45∘.
Hence the supplementary angles are:
180∘−90∘=90∘
180∘−45∘=135∘
180∘−45∘=135∘
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Each difference: 1 Mark
1. A line is a set of points that can be extended in either direction whereas a line segment is a part of a line, which is bounded between two given points.
2. Length of a line segment can be measured, whereas a line can extend up to infinity and cannot be measured.
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Steps: 1 Mark
Result: 1 Mark
The number of endpoints in a line is zero.
⇒X=0
The number of endpoints in a Ray is 1
⇒Y=1
The number of endpoints in a line segment is 2.
⇒Z=2
∴X+Y+Z=3
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Solution: 1 Mark each
(a) Sum of the angles should be equal to 360∘
110∘+60∘+40∘+x∘=360∘
210∘+x∘=360∘
⇒x∘=360∘−210∘=150∘
(b) Let A and B be two complementary angles and let A > 45∘.
A + B = 90∘
B = 90∘ − A
Therefore, B will be less than 45∘.
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Concept: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Sum of the angles of a triangle is 180∘.
Since OC = OD, ∠OCD=∠ODC=30∘
[Angles opposite to equal sides are equal]
⇒∠COD=180∘−(30∘+30∘)=120∘
∠AOB=∠COD [Vertically Opposite Angles]
∴∠AOB=120∘
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(a) Steps: 1 Mark
Proof: 1 Mark
(b) Solution: 1 Mark
(a) ∠XPB=∠MSP=k (Alternate Angles are equal)
⇒LX∥MY...(i).
∠PSM=∠SRN=k (Corresponding Angles)
⇒MY∥NZ....(ii).
From (i) and (ii)
LX∥MY and MY∥NZ
⇒LX∥MY∥NZ.
(b) Given k=50∘,
∠PSY=180∘−k
=180∘−50∘=130∘
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(a) Steps: 1 Mark
Proof: 1 Mark
(b) Solution: 1 Mark
(a) Given, ∠LST=105∘ and ∠NTS=75∘
∠LST+∠NTS=105∘+75∘=180∘
These are co-interior angles.
Since co-interior angles are supplementary, lines are parallel.
Hence, the lines LM and NQ are parallel.
(b) Since AB is parallel to CD, corresponding angles will be equal.
Therefore, x = 130°
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(a) Steps: 2 Marks
Result: 1 Mark
(b) Solution: 1 Mark
(a) Since AB∥CD
⇒∠BAC+∠DCA=180∘
[Sum of Co-interior angles is equal to 180∘]
⇒∠BAC2+∠DCA2=180∘2
⇒∠OAC+∠OCA=90∘ [AD & BC are angle bisectors]
In ΔAOC,
∠AOC+∠OAC+∠OCA=180∘
[sum of all the angles in triangle is 180∘]
⇒∠AOC=180∘−90∘=90∘
∠AOC=∠BOD [Vertically Opposite Angles]
⇒∠BOD=90∘
(b) The value of an exterior angle of a triangle is equal to the sum of the opposite interior angles.
As the exterior angle value is given to be 120∘, the sum of the two interior angles is also 120∘.
Thus, (x+y) = 120∘