Question

If two angles are complementary and one angle is 10°greater than the other, then find the smaller angle.

Answer 1

Let the smaller angle be X
Now bigger angle = X+10°
X+X+10° = 90°
2X=90° -10°
2X= 80°
X=80°/2
X=40°
Small angle = 40°
Big angle =50°



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Answer 2

If two angles are complementary and one angle is 10 degrees greater than the other, then the smaller angle is 40 degrees

Solution:

Given that two angles are complementary

Let the smaller complementary angle be "a"

Let the larger complementary angle be "b"

Two Angles are Complementary when they add up to 90 degrees

So we can say,

smaller complementary angle + larger complementary angle = 90

a + b = 90 --- eqn 1

Also given that one angle is 10 degree greater than other

b = a + 10 --- eqn 2

Substitute eqn 2 in eqn 1

a + a + 10 = 90

2a = 80

a = 40

From eqn 2,

b = 40 + 10

b = 50

Thus the smaller angle is 40 degrees

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