If angle A is three times as large as angle B, and angles B and C sum to 90 degrees, what is the measure of each angle?

1 Answer
Sep 12, 2015

Answer:

#"A"=90º#
#"B"=30º#
#"C"=60º#

Explanation:

We are given :
#color(red)((1))" A"=3"B"#
and #color(red)((2))" B"+"C"=90º#

Assuming that all these angles are part of the same triangle

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  • All the angles in a triangle sum to #180º#

#=>color(red)((3))" A"+"B"+"C"=180º#

Put #color(red)((2))# in #color(red)((3))#
#=>"A"+90º=180º=>"A"=90º#

Put the value of #"A"# in #color(red)((1))#
#=>90º=3"B"=>"B"=30º#

Put the value of #"B"# in #color(red)((2))#
#=>30º+"C"=90º=>"C"=60º#