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Question

Find the value of the unknown interior angle x in the following figures:
1060828_b1e850ef90494e8195a7d413b498ae71.png

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Solution


For fig (i)
BCA+ACD=180o [ Linear pair ]
BCA+115o=180o
BCA=180o115o=65o
In ABC,
ABC+BCA+CAB=180o
x+65o+50o=180o
x+115o=180o
x=180o115o=65o

For fig (ii)
PRQ+QRS=180o [ Linear pair ]
PRQ+100o=180o
PRQ=180o100o=80o
In PQR,
PRQ+RQP+QPR=180o
80o+x+70o=180o
150o+x=180o
x=180o150o=30o

For fig (iii),
NLM+KLN=180o
NLM+1250o=180o
NLM=180o125o=55o
In LMN,
LMN+MNL+NLM=180o
90o+x+55o=180o
145o+x=180o
x=180o145o=35o

998475_1060828_ans_3023be211f3e47949e291299603781bb.png

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