Find the values for x and y

Mathematics

2 answers:

mel-nik [20]3 years ago

4 0

Both form straight angles, which are 180 degrees.

x+4y+x+y=180
2x+5y=180

4x+y=180

Solve the second equation for y and substitute the variable.
y= -4x+180

2x+5(-4x+180)=180
2x-20x+900=180
-18x= -720
x=40

Plug the x value in
4(40)+y= 180
160+y=180
y=20

Final answer: x=40, y=20

Assoli18 [71]3 years ago

3 0

X+4y+x+y= 4x+y=180
simplify by adding like terms
2x+5y= 4x+y=180
Subtract y from each side
2x+4y=4x=180
Subtract 2x from each side
4y=2x=180
y=180/4=45
x=180/2=90

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In the above figure (not drawn to scale), Find ∠AEC.

n200080 [17]

Answer:

C. 75°

Step-by-step explanation:

We have been given a circle and we are asked to find the measure of angle AEC.

We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.

$m\angle AEC=\frac{110^o+40^o}{2}$