The larger of two supplementary angles exceeds 7 times the smaller by 4 degrees. What is the measure of the larger angle?

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Answer 1 · 2015-11-19T12:06:13

The measure of larger angle#=158^o#

Let's take:
Larger Angle#=L#
Smaller Angle#=S#

If these two angles are supplementary, it means:
#L+S=180^o ..........(i)#

It is given #L# exceeds 7 times of #S# by 4 degrees, i.e.
#L=(7xxS)+4=7S+4#

Now put the above value of #L# in #eq.(i)#
#(7S+4)+S=180^o#
=> #8S+4=180#
=> #8S=180-4#
=> #8S=176#
=> #S=176-:8#
=> #S=22^o#

Now we can find the value of #L# from #eq.(i)# as:
#L=180^o-S=180^o-22^o=158^o#