Question

The ratio of the complementary and supplementary angles of angle m is 1:6
What is the measure of angle M?​

Answer 1

Answer:

1x+6x= 180+90,7x=270

Answer 2

The measure of angle m=72 degree

Step-by-step explanation:

Let x and y are complementary and supplementary angles of angle m.

By definition of complementary angle

$x+\angle m=90^{\circ}$

$x=90-\angle m$..(1)

By definition of supplementary angle

$y+\angle m=180^{\circ}$

$y=180-\angle m$...(2)

According to question

$x:y=1:6$

$\frac{90-\angle m}{180-\angle m}=\frac{1}{6}$

$540-6\angle m=180-\angle m$

$540-180=6\angle m-\angle m$

$360=5\angle m$

$\angle m=\frac{360}{5}=72^{\circ}$

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