Two angles measuring p and q are complementary If 3p2q40 ca

Two angles measuring p and q are complementary . If 3p-2q=40 calculate the measure of smaller angle.

Solution

According to the rule, 2 angles are complementary if their sum is 90 degree.

So, we\'ll write mathematically the condition:

p + q = 90 (1)

We also have, from enunciation, that:

3p-2q = 40 (2)

We\'ll multiply (1) by 2:

2p + 2q = 180 (3)

We\'ll add (3) to (2):

2p + 2q + 3p - 2q = 180 + 40

We\'ll combine and eliminate like terms:

5p = 220

We\'ll divide by 5:

p = 44 degrees

We\'ll calculate q.

p + q = 90

44 + q = 90

We\'ll subtract 44 and we\'ll gte:

q = 46 degrees

We notice that the smaller measure is the one of the angle p.

p = 44 degrees.