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Masteriza [31]
3 years ago
14

In the figure above, quadrilateral ABCD is a parallelogram. Let x represent the measure of angle GBF, y represent the measure of

angle CBE, and z represent the measure of angle BCE.

Mathematics
1 answer:
ira [324]3 years ago
8 0
Answers:
measure angle x = 40°
measure angle y = 35°
measure angle z = 55°

Explanation:
Part (a): getting angle x:
In triangle BED, we have:
measure angle BED = 90°
measure angle BDE = 50°
Therefore:
measure angle DBE = 180 - (90+50) = 40°
Now, we have angle DBE and angle GBF vertically opposite angles.
This means that they are both equal. Therefore angle GBF = 40°
Since angle GBF is x, therefore:
x = 40°

Part (b): getting angle y:
We know that the sum of measures of angles on a straight line is 180.
This means that:
angle GBF + angle GBC + angle CBE = 180
We have:
angle GBF = 40°
angle GBC = 105°
angle CBE = y
Therefore:
40 + 105 + y = 180
y = 35°

Part (c): getting angle z:
In triangle BCE, we have:
measure angle BCE = z
measure angle BEC = 90°
measure angle CBE = 35°
Therefore:
z + 90 + 35 = 180
z = 55°

Hope this helps :)

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Lubov Fominskaja [6]

Answer:

F = 1.8C +32

F = 86^{\circ}F

Step-by-step explanation:

Represent Celsius with C and Fahrenheit with F.

So, we have:

(C_1,F_1) = (100,212)

(C_2,F_2) = (0,32)

Solving (a): Represent as a linear equation

First, we calculate the slope:

m = \frac{F_2 - F_1}{C_2 - C_1}

This gives:

m = \frac{32 - 212}{0 - 100}

m = \frac{-180}{- 100}

m = 1.8

The linear equation is then calculated using:

F - F_1 = m(C -C_1)

Where

(C_1,F_1) = (100,212)

m = 1.8

F - 212 = 1.8(C -100)

F - 212 = 1.8C -180

Make F the subject

F = 1.8C -180+212

F = 1.8C +32

Solving (b): The value of F when C = 30

Substitute 30 for C in F = 1.8C +32

F = 1.8 * 30 + 32

F = 54 + 32

F = 86

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