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elena-14-01-66 [18.8K]
2 years ago
11

A and b are complementary angles. a measures 32º. What is the measure of b?

Mathematics
1 answer:
Trava [24]2 years ago
5 0

Answer:

A = 32º and B = 58º

Step-by-step explanation:

A complementary angle measures at 90º. If angle A is 32º, we can write an equation to solve for B.

32 + B = 90

32 - 32 + B = 90 - 32

B = 58

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Find the value of 3x + 2 when 7 + x = 5
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6) If a square is 8 inches on each side, what is its area? _______ square inches
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If each quadrilateral below is a parallelogram, find the missing measures.
prisoha [69]

Step-by-step explanation:

We will use parallelogram properties to answer our given problems.

(1) Since we know that opposite sides of parallelogram are congruent, therefore measure of side MN and side KN will be equal to the measure of their opposite sides.

LM=KN   and   KL=MN

Upon substituting our given values we will get,

45=KN   and   31=MN

Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.

We have been given m\angle N=119^{o}, therefore m\angle L=119^{o}.

We will find measure of angle K by using supplementary angles.

m\angle N+m\angle M=180^{o}

119^{o}+m\angle M=180^{o}

m\angle M=(180-119)^{o}

m\angle M=61^{o}

By opposite angles of parallelogram m\angle K=61^{o}.

(2) Opposite sides of parallelogram are equal. Therefore, CF=DE and FE=CD.

Upon substituting our given values we will get,

CF=10  and FE=15.

Property: Diagonals of parallelogram bisect each other.

So CE will be 2 times CG and GD will be half the length of FD.

CE=2\times 7=14

GD=\frac{1}{2}\times 22=11

(3) Property: Opposite sides of parallelogram are congruent.

SR=PQ   and   QR=PS

Upon substituting our given values we will get,

SR=24   and   QR=19

Property: Diagonals of parallelogram bisect each other.

So SQ will be 2 times TQ and PT will be half the length of PR.

SQ=2\times 10=20

PT=\frac{1}{2}\times 42=21

Property: The opposite angles of parallelogram are congruent and consecutive angles are supplementary.

m\angle PQR=106^{o}

m\angle PQS=m\angle QSR  Alternate interior angles.

m\angle PQS=49^{o}

m\angle QRS=m\angle QPS Opposite angles of parallelogram.

m\angle PQR+m\angle QPS=180^{o}

106^{o}+m\angle QPS=180^{o}

m\angle QPS=180^{o}-106^{o}

m\angle QPS=74^{o}

Therefore, measure of angle QRS will 74 degrees.

m\angle PRS=m\angle QPR Alternate interior angles.

35^{o}=m\angle QPR

m\angle RPS=74^{o}-m\angle QPR

m\angle RPS=74^{o}-35^{o}

m\angle RPS=39^{o}

Now let us find measure of angle PSQ.

m\angle PSQ=m\angle PQR-m\angle QSR

m\angle PSQ=106^{o}-49^{o}

m\angle PSQ=57^{o}

The image is not clear, so I am unable to answer the last two problems.



5 0
3 years ago
Read 2 more answers
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