Х 71 - 3b
R
- 10b + 113
?
Find the measure for LQR.
A)
125
B)
127
C)
129°
D)
133
Geometry

B. 127°

Step-by-step explanation:

First, use the vertical angles XQL and MQR to find the value of b.

Vertical angles are congruent.

71 - 3b = -10b + 113

7b = 42

b = 6

m<XQL = -10b + 113 = -10(60) + 113 = 53

Angles XQL and LQR form a linear pair, so they are supplementary.

m<XQL + m<LQR = 180

53 + m<LQR = 180

m<LQR = 127

B. 127°

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

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step-by-step explanation: