Question

Please help me!
Look at this diagram.

Answer 1

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

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

Answer 2

`x=13\text{ and } y=5`

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 x = 13:

`10y+6(13)+52=180`

Simplify:

`10y+130=180`

Therefore:

`10y=50`

And by dividing both sides by 10:

`y=5`