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3 years ago

Angle A and angle B are complementary angles. If m angle A = (6x – 8)° and m

Mathematics

1 answer:

In-s [12.5K]3 years ago

3 0

Answer: B = 56 degrees

Step-by-step explanation: Complementary angles add up 90 degrees. So we will set both of the equations equal to 90 degrees and then solve from there.

6x+8+5x+21=90

1. Simplify 5x + 6x and 21 - 8

11x+13=90

2. Subtract 13 from both sides.

11x=90-13

3. Simplify 90-13 to 77.

11x=77

4. Divide both sides by 11.

x = 77/11

5. Simplify 77/11 to 7

x=7

Now we have to take the value of x and substitute it back into B = (5x+21)

1. Substitute

B = (5(7)+21)

B = 35 +21

B = 56

HOPE THIS HELPS :)

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To solve this problem we will use Heron's formula:

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Also:

$(I) \ PS=SQ \\ \\ (II) \ SQ-PQ = 1 \\ \\ (III) \ PS+PQ+SQ=50 \\ \\ \\ (I) \ into \ (III): \\ \\ SQ+PQ+SQ=50 \\ \\ \therefore (IV) \ 2SQ+PQ=50 \\ \\ From \ (II): \\ \\ PQ=SQ-1 \\ \\ (II) \ into \ (IV): \\ \\ 2SQ+(SQ-1)=50 \\ 3SQ-1=50 \\ 3SQ=51 \\ \\ \boxed{SQ=17} \\ \\ \boxed{PS=17} \\ \\ PQ=SQ-1=17-1 \therefore \boxed{PQ=16}$

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$A=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ A=\sqrt{s(s-PS)(s-SQ)(s-PQ)} \\ \\ A=\sqrt{s(s-17)(s-17)(s-16)} \\ \\ A=\sqrt{25(25-17)(25-17)(25-16)} \\ \\ \boxed{A=120}$

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