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Nikitich [7]
2 years ago
14

Please help me! Look at this diagram.

Mathematics
2 answers:
Rina8888 [55]2 years ago
8 0

Answer:

if you look at carefully the left triangle has two same side. so left-angle of C is 180-130=50 degree 5x+5x+50=180 x=13 degree

Step-by-step explanation:

for right triangle again one angle is 50 degree and other is 6*13-(3)=75 degree so 75+50+(10y+5)=180 degree y=5 degree

Gnom [1K]2 years ago
5 0

Answer:

x=13\text{ and } y=5

Step-by-step explanation:

First, notice that ∠BCD and ∠DCE form a linear pair. Linear pairs sum to 180°. Therefore:

m\angle BCD + m\angle DCE = 180

And since we know that ∠BCD measures 130°:

m\angle DCE  = 180-130=50^\circ

And since ∠DCE and ∠BCA are vertical angles:

\displaystyle \angle DCE \cong  \angle BCA

Therefore, by definition:

m\angle DCE = m\angle BCA = 50^\circ

Looking at the left triangle, we can see that BC and AC both have one tick mark. This means that they are congruent. Therefore, ΔABC is an isosceles triangle. The two base angles of an isosceles triangle are congruent. Hence:

m\angle A = m\angle B

The interior angles of a triangle must total 180°. So:

m\angle A + m\angle B +m\angle BCA = 180

Substitute in known values:

m\angle A + m\angle A+ (50)=180

Simplify:

2m\angle A=130

Divide both sides by two:

m\angle A = 65

Substitute:

(5x)=65

Therefore:

x=13

Similarly, for the triangle on the right, we can write that:

m\angle D + m\angle E + m\angle DCE = 180

Substitute:

(10y+5)+(6x-3)+(50)=180

Combine like terms:

10y+6x+52=180

Since we determined that <em>x</em> = 13:

10y+6(13)+52=180

Simplify:

10y+130=180

Therefore:

10y=50

And by dividing both sides by 10:

y=5

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