Question

12.
13.
14.
15.
please find the measures of the missing angles. draw a picture to help organize your
thoughts.

1. the ( m angle a ) is complementary to the ( m angle b ). the ( m angle c ) is complementary to the ( m angle b ).

if ( m angle a = 62^{circ} ), what is the ( m angle b ) and the ( m angle c )?

1. the ( m angle d ) is supplementary to the ( m angle e ). the ( m angle f ) is supplementary to the ( m angle e ).

if ( m angle f = 113^{circ} ), what is the ( m angle d ) and the ( m angle e )?

Explanation:

12.

Step1: Use supplementary angles property

Supplementary angles sum to \(180^{\circ}\). So, \(149^{\circ}+(13x + 5)^{\circ}=180^{\circ}\)

$$149+13x + 5=180$$

$$13x+154 = 180$$

Step2: Solve for \(x\)

Subtract \(154\) from both sides: \(13x=180 - 154\)

$$13x=26$$

Divide both sides by \(13\): \(x = 2\)

13.

Step1: Use complementary angles property

Complementary angles sum to \(90^{\circ}\). So, \((8x + 5)^{\circ}+(3x + 8)^{\circ}=90^{\circ}\)

$$8x+5+3x + 8=90$$

$$11x+13 = 90$$

Step2: Solve for \(x\)

Subtract \(13\) from both sides: \(11x=90 - 13\)

$$11x=77$$

Divide both sides by \(11\): \(x = 7\)

14.

Step1: Use supplementary angles property

Supplementary angles sum to \(180^{\circ}\). So, \((15x-12)^{\circ}+(5x - 18)^{\circ}=180^{\circ}\)

$$15x-12+5x - 18=180$$

$$20x-30 = 180$$

Step2: Solve for \(x\)

Add \(30\) to both sides: \(20x=180 + 30\)

$$20x=210$$

Divide both sides by \(20\): \(x = 10.5\)

15.

Step1: Use supplementary angles property

Supplementary angles sum to \(180^{\circ}\). So, \((6x + 13)^{\circ}+(14x-33)^{\circ}=180^{\circ}\)

$$6x+13+14x - 33=180$$

$$20x-20 = 180$$

Step2: Solve for \(x\)

Add \(20\) to both sides: \(20x=180 + 20\)

$$20x=200$$

Divide both sides by \(20\): \(x = 10\)

16.

Step1: Find \(m\angle B\)

Since \(\angle A\) is complementary to \(\angle B\), \(m\angle A+m\angle B = 90^{\circ}\). Given \(m\angle A = 62^{\circ}\), then \(62^{\circ}+m\angle B=90^{\circ}\), so \(m\angle B=90 - 62=28^{\circ}\)

Step2: Find \(m\angle C\)

Since \(\angle C\) is complementary to \(\angle B\), \(m\angle C+m\angle B = 90^{\circ}\). Substitute \(m\angle B = 28^{\circ}\), then \(m\angle C=90 - 28=62^{\circ}\)

17.

Step1: Find \(m\angle E\)

Since \(\angle F\) is supplementary to \(\angle E\), \(m\angle F+m\angle E = 180^{\circ}\). Given \(m\angle F = 113^{\circ}\), then \(113^{\circ}+m\angle E=180^{\circ}\), so \(m\angle E=180 - 113 = 67^{\circ}\)

Step2: Find \(m\angle D\)

Since \(\angle D\) is supplementary to \(\angle E\), \(m\angle D+m\angle E = 180^{\circ}\). Substitute \(m\angle E = 67^{\circ}\), then \(m\angle D=180 - 67=113^{\circ}\)

Answer:

1. \(x = 2\) (Supplementary)
2. \(x = 7\) (Complementary)
3. \(x = 10.5\) (Supplementary)
4. \(x = 10\) (Supplementary)
5. \(m\angle B = 28^{\circ}\), \(m\angle C = 62^{\circ}\)
6. \(m\angle D = 113^{\circ}\), \(m\angle E = 67^{\circ}\)