Question

examples 17 - 18: find the measure of each angle.

1. given that ∠1 is a complement of ∠2

and m∠1 = 64°, find m∠2.

1. given that ∠3 is a supplement of ∠4

and m∠4 = 28°, find m∠3.

practice 19 - 20: find the measure of each angle.

1. given that ∠1 is a complement of ∠2

and m∠1 = 47°, find m∠2.

1. given that ∠3 is a supplement of ∠4

and m∠4 = 106°, find m∠3.

examples 21 - 22: use the given information to find the measure of each angle.

1. ∠a and ∠b are complementary. if m∠a=(3x+2)° and m∠b=(x-4)°, find m∠a and m∠b.

1. ∠a and ∠b are supplementary. if m∠a=(8x+100)° and m∠b=(2x+50)°, find m∠a and m∠b.

practice 23 - 24: use the given information to find the measure of each angle.

1. ∠a and ∠b are complementary. if m∠a=(6x-15)° and m∠b=(3x+6)°, find m∠a and m∠b.
2. ∠a and ∠b are supplementary. if m∠a=(18x-1)° and m∠b=(23x+17)°, find m∠a and m∠b.

Explanation:

17. Step1: Recall complementary angle sum

Complementary angles sum to $90^\circ$.

17. Step2: Calculate $m\angle2$

$m\angle2 = 90^\circ - m\angle1 = 90^\circ - 64^\circ$

18. Step1: Recall supplementary angle sum

Supplementary angles sum to $180^\circ$.

18. Step2: Calculate $m\angle3$

$m\angle3 = 180^\circ - m\angle4 = 180^\circ - 28^\circ$

19. Step1: Use complementary angle rule

Complementary angles sum to $90^\circ$.

19. Step2: Calculate $m\angle2$

$m\angle2 = 90^\circ - m\angle1 = 90^\circ - 47^\circ$

20. Step1: Use supplementary angle rule

Supplementary angles sum to $180^\circ$.

20. Step2: Calculate $m\angle3$

$m\angle3 = 180^\circ - m\angle4 = 180^\circ - 106^\circ$

21. Step1: Set up complementary angle equation

$(3x+2) + (x-4) = 90$

21. Step2: Simplify and solve for $x$

$4x - 2 = 90 \implies 4x = 92 \implies x = 23$

21. Step3: Calculate $m\angle A$ and $m\angle B$

$m\angle A = 3(23)+2 = 71^\circ$, $m\angle B = 23-4 = 19^\circ$

22. Step1: Set up supplementary angle equation

$(8x+100) + (2x+50) = 180$

22. Step2: Simplify and solve for $x$

$10x + 150 = 180 \implies 10x = 30 \implies x = 3$

22. Step3: Calculate $m\angle A$ and $m\angle B$

$m\angle A = 8(3)+100 = 124^\circ$, $m\angle B = 2(3)+50 = 56^\circ$

23. Step1: Set up complementary angle equation

$(6x-15) + (3x+6) = 90$

23. Step2: Simplify and solve for $x$

$9x - 9 = 90 \implies 9x = 99 \implies x = 11$

23. Step3: Calculate $m\angle A$ and $m\angle B$

$m\angle A = 6(11)-15 = 51^\circ$, $m\angle B = 3(11)+6 = 39^\circ$

24. Step1: Set up supplementary angle equation

$(18x-1) + (23x+17) = 180$

24. Step2: Simplify and solve for $x$

$41x + 16 = 180 \implies 41x = 164 \implies x = 4$

24. Step3: Calculate $m\angle A$ and $m\angle B$

$m\angle A = 18(4)-1 = 71^\circ$, $m\angle B = 23(4)+17 = 109^\circ$

Answer:

1. $m\angle2 = 26^\circ$
2. $m\angle3 = 152^\circ$
3. $m\angle2 = 43^\circ$
4. $m\angle3 = 74^\circ$
5. $m\angle A = 71^\circ$, $m\angle B = 19^\circ$
6. $m\angle A = 124^\circ$, $m\angle B = 56^\circ$
7. $m\angle A = 51^\circ$, $m\angle B = 39^\circ$
8. $m\angle A = 71^\circ$, $m\angle B = 109^\circ$