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6. Find the measure of an angle, if 7 times its complement is 10 less than 3 1
0
times its supplement.
Ans: 25
0
7. In figure, if AB || CD || EE, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then find ∠QRS. 2
Solution:
Given, PQ || RS
∠PQC = ∠BRS = 60° [alternate exterior angles and ∠PQC = 60° (given)] and
∠DQR = ∠QRA = 25° [alternate interior angles]
[∠DQR = 25°, given]
∠QRS = ∠QRA + ∠ARS
= ∠QRA + (180° – ∠BRS) [linear pair axiom]
= 25° + 180° – 60°= 205° – 60°= 145°
8. In the figure, BA || ED and BC || EF. Show that ∠ABC = ∠DEF. 2
Solution:
Given BA || ED and BC || EF.
To show ∠ABC = ∠DEF.
Construction Draw a ray EP opposite to ray ED.
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