Question

I need help with 29 , 32, 33

Answer 1

29) m∠A = 83°

m∠B = 7°

32) m∠A = 103°

m∠B = 77°

33) m∠A = 24°

m∠B = 156°

Explanation:

Question 29

Complementary angles: Two angles whose measures sum to 90°.

`\implies m \angle A + m \angle B=90^(\circ)`

`\implies (16x - 13)^(\circ) + (2x - 5)^(\circ)=90^(\circ)`

`\implies 16x - 13 + 2x - 5=90`

`\implies 18x -18=90`

`\implies 18x =108`

`\implies x=6`

Substitute the found value of x into the expression for angle A:

`\implies m \angle A = \left(16 \cdot 6 - 13 \right)^(\circ)`

`\implies m \angle A = \left(96 - 13 \right)^(\circ)`

`\implies m \angle A = 83^(\circ)`

As the sum of angles A and B is 90°:

`\implies m \angle B = 90^(\circ)-m \angle A`

`\implies m \angle B = 90^(\circ)-83^(\circ)`

`\implies m \angle B = 7^(\circ)`

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Question 32

Supplementary angles: Two angles whose measures sum to 180°.

`\implies m \angle A + m \angle B=180^(\circ)`

`\implies (x+11)^(\circ) + (x-15)^(\circ)=180^(\circ)`

`\implies x+11+ x-15=180`

`\implies 2x-4=180`

`\implies 2x=184`

`\implies x=92`

Substitute the found value of x into the expression for angle A:

`\implies m \angle A = \left(92+11 \right)^(\circ)`

`\implies m \angle A =103^(\circ)`

As the sum of angles A and B is 180°:

`\implies m \angle B = 180^(\circ)-m \angle A`

`\implies m \angle B = 180^(\circ)-103^(\circ)`

`\implies m \angle B = 77^(\circ)`

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Question 33

Supplementary angles: Two angles whose measures sum to 180°.

`\implies m \angle A + m \angle B=180^(\circ)`

`\implies (9x-12)^(\circ) + (24x+60)^(\circ)=180^(\circ)`

`\implies 9x-12+24x+60=180`

`\implies 33x+48=180`

`\implies 33x=132`

`\implies x=4`

Substitute the found value of x into the expression for angle A:

`\implies m \angle A = \left(9 \cdot 4-12 \right)^(\circ)`

`\implies m \angle A = \left(36-12 \right)^(\circ)`

`\implies m \angle A =24^(\circ)`

As the sum of angles A and B is 180°:

`\implies m \angle B = 180^(\circ)-m \angle A`

`\implies m \angle B = 180^(\circ)-24^(\circ)`

`\implies m \angle B = 156^(\circ)`