Question

consider this
angles are complementary if the sum of their measures is 90°. angles are supplementary if the sum of their measures is 180°.
find x.
1
2
3
4
5
6

Explanation:

1. For the first pair of complementary angles:

• Step1: Use the complementary angle property

Complementary angles sum to \(90^{\circ}\). So, \(x + 62=90\).

• Step2: Solve for \(x\)

Subtract \(62\) from both sides: \(x=90 - 62\).

2. For the second pair of supplementary angles:

• Step1: Use the supplementary angle property

Supplementary angles sum to \(180^{\circ}\). So, \(x + 98=180\).

• Step2: Solve for \(x\)

Subtract \(98\) from both sides: \(x=180 - 98\).

3. For the third pair of supplementary angles:

• Step1: Use the supplementary angle property

\(58+2x = 180\).

• Step2: Isolate the term with \(x\)

Subtract \(58\) from both sides: \(2x=180 - 58\), so \(2x = 122\).

• Step3: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{122}{2}\).

4. For the fourth pair of complementary angles:

• Step1: Use the complementary angle property

\(x + 15=90\).

• Step2: Solve for \(x\)

Subtract \(15\) from both sides: \(x=90 - 15\).

5. For the fifth pair of supplementary angles:

• Step1: Use the supplementary angle property

\(x+x = 180\), which simplifies to \(2x=180\).

• Step2: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{180}{2}\).

6. For the sixth pair of complementary angles:

• Step1: Use the complementary angle property

\(x + 2x=90\), which simplifies to \(3x=90\).

• Step2: Solve for \(x\)

Divide both sides by \(3\): \(x=\frac{90}{3}\).

Answer:

1. \(x = 28\)
2. \(x = 82\)
3. \(x = 61\)
4. \(x = 75\)
5. \(x = 90\)
6. \(x = 30\)