Respuesta :

bearbearxx1

Answer:

1. x = 20

2. x = 3

3. RST = 22 degrees

Step-by-step explanation:

1. Since QR bisects PQS, the measure of the angles PQR and PQS should be equal, so we can set their expressions equal to each other, and then solve.

4x-10 = -3x+130

4x = -3x +140

7x = 140

x = 20

2. Since there is a CAB has a right angle, the measure of angles CAD and BAD should add up to 90 degrees. So we can set the sum of their expressions equal to 90 degrees.

(5x+57) + (x+15) = 90

6x + 72 = 90

6x = 18

x = 3

3. I can't see where the R is but if it is on the empty line then we can find RST by subtracting the measure of angle TSU from angle RSU.

TSU - RSU = RST

91 - 69 = 22 degrees

RST = 22 degrees

semsee45

Answer:

7.  m∠PQR =70°   m∠PQS = 140°

8.  m∠CAD = 18°    m∠BAD = 72°

9.  m∠RST = 22°

Step-by-step explanation:

Question 7

If QR bisects (divides into two equal parts) ∠PQS then:

⇒ m∠PQR = m∠RQS

⇒ 4x - 10 = -3x + 130

⇒ 4x - 10 + 10 = -3x + 130 + 10

⇒ 4x = -3x + 140

⇒ 4x + 3x = -3x + 140 + 3x

⇒ 7x = 140

⇒ 7x ÷ 7 = 140 ÷ 7

⇒ x = 20

Substitute the found value of x into the expression for m∠PQR:

⇒ m∠PQR = 4(20) - 10 = 70°

As QR bisects ∠PQS:

⇒ m∠PQS = 2m∠PQR = 2 × 70° = 140°

Question 8

From inspection of the given diagram, ∠BAC = 90°.

⇒ m∠CAD + m∠BAD = 90

⇒ x + 15 + 5x + 57 = 90

⇒ 6x + 72 = 90

⇒ 6x + 72 - 72 = 90 - 72

⇒ 6x = 18

⇒ 6x ÷6 = 18 ÷ 6

⇒ x = 3

Substitute the found value of x into the expressions for the two angles:

⇒ m∠CAD = 3 + 15 = 18°

⇒ m∠BAD = 5(3) + 57 = 72°

Question 9

From inspection of the given diagram (and assuming R is on the empty line segment):

   m∠RSU = m∠RST + m∠TSU

⇒ 91° = m∠RST + 69°

⇒ 91° - 69° = m∠RST + 69° - 69°

⇒ 22° = m∠RST

⇒ m∠RST = 22°

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