Question

Pls help me im bad a geometry pls help

Answer 1

Answer:

1)∠DOF, with F (-5,-1) 2) x=30º y=90º 3)∠x=∠y=50º 4) a)x=35º b=110º 5) x=14 y=15 6) ∠EIG≅FIH and ∠EIF ≅ ∠GIH 7) True because of ∠ABC=∠XYZ

Step-by-step explanation:

1) Supplementary angles: two angles whose sum is equivalent to 180º. Adjacent angles share the same vertex. So DOF measures 135º.

2) Vertical Angles Theorem assures us that 2x= y-x. Moreover to that, 2x+(y+x) =180º And (y+x)+(y-x)=180º

I) 2x=y-x ∴3x=y

II) (y+x)+(y-x)=180º If 2y=180º → y =90º

If 3x=y and 3x=90 → x=30

3) By the Vertical Angle theorem, two angles sharing the same vertex and opposite are congruent. Also, the ∠x +40º are complementary angles, i.e. their sum is equal to 90º.

Then x =y

So ∠x=∠y=50º

4)

a) Similarly to the 1st case:

y=2x (Vertical Angles Theorem)

2x+(x+y+5)=180 (Supplementary Angles)

Algebraically.

Then, let's solve a Linear System of Equations.

2x-y=0

3x+y=175

----------------

5x =175 ∴ x=35

If y=2x Then y=70º

b) The Unlabeled angle it's equal to (x+y+5) according to  Vertical Angle Theorem

So 35+70+5=105+5=110º

5) Similarly to 1st case, and to the previous one:

a)1) 3x+8=5x-20

2) 3x+8+5x+4y=180 ∴ 8x +4y=172

-2x+28=0 *4

8x+4y=172

--------------------

-8x+0=-112

8x+4y=172

-----------------

4y=60

y=15 and 8x +60=172 ∴ 8x=112 x=14

6)

∠EIG≅FIH and ∠EIF ≅ ∠GIH For the first both pairs share the same vertex, the first one is perpendicular and the second one by the Vertical Theorem.

7) If Supplementary angles the first one measures the same as the second one then ∠ABC=∠XYZ = So we can say that's true, since the only positive integers, with the same value that sums up to 180º, is 90º + 90º

Answer 2

I would say x=30 y=90

because

(y+x)
90+30=120

(y-x)
90-30=60

the sum of those 2 angles should equal 180 because they are supplementary angle.

120+60=180

and because the angles of 2x and y+x are also supplementary they should equal 180


2x
2(30)
=60

(y+x)
90+30
=120

120+60=180