Describing Angles

We have two complementary angles called

∠ A

and

∠ B .

We can write the sum and difference of the angle measures.

m ∠ A + m ∠ B m ∠ A - m ∠ B

The sum of the measures of the angles is

5 2^{\circ}

greater than the difference between the measures. Therefore we can write an equation using the expressions for the sum and the difference.

m ∠ A - m ∠ B + 5 2^{\circ} = m ∠ A + m ∠ B

Let us use this to find

m ∠ B .

m ∠ A - m ∠ B + 5 2^{\circ} = m ∠ A + m ∠ B

LHS - m ∠ A = RHS - m ∠ A

- m ∠ B + 5 2^{\circ} = m ∠ B

LHS + m ∠ B = RHS + m ∠ B

5 2^{\circ} = 2 \cdot m ∠ B

LHS / 2 = RHS / 2

2 6^{\circ} = m ∠ B

RearrangeEqnRearrange equation

m ∠ B = 2 6^{\circ}

Since

∠ A

and

∠ B

are complementary the sum of their measures is

9 0^{\circ} .

m ∠ A + m ∠ B = 9 0^{\circ}

m ∠ B = 2 6^{\circ}

m ∠ A + 2 6^{\circ} = 9 0^{\circ}

LHS - 2 6^{\circ} = RHS - 2 6^{\circ}

m ∠ A = 6 4^{\circ}

Exercise 1.18 - Solution