I'm Using my last points will give brainliest geometry - finding angles with justification (level 1) delta math Please do step by step and pick reasoning for each
here are reasonings to pick from:

verticle angles

Linear pair (or triples)

Congruent angles

sum of angles in a triangle

sum of angles in a quadrilateral

Base angles of an isosceles triangle

Angle bisector definition

corresponding angles

alternate interior angles

alternate exterior angles

same - side interior angles

angle addition postulate

angle subtraction postulate

perpendicular lines form right angles

In the diagram shown, if m<AGF  =  64°, m<CGE  =  84°, then m<DGB    =    32°

From the figure shown:

m<AGF  =  64° (Given)

m<CGE  =  84° (Given)

m<AGF   =  m<BGE  (Vertically opposite angles are equal)

m<AGF  =  m<BGE   =  64°

m<CGE  +  m<BGE  +  m<DGB   =  180° (Sum of angles on a straight line)

84   +  64  +   m<DGB   =   180

148   +   m<DGB    =   180

m<DGB    =   180   -  148

m<DGB    =    32°

Therefore, in the diagram shown, if m<AGF  =  64°, m<CGE  =  84°, then m<DGB    =    32°

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m∠AGF + m∠CGE + m∠AGC = 180° ( linear pair )

84° + 64° + m∠AGC = 180°

148° + m∠AGC = 180°

m∠AGC = 180 - 148

m∠AGC = 32°

As m∠AGC and m∠DGB are vertically opposite angles , their angle measure will be equal .

Which means :-

m∠AGC = m∠DGB ( vertically opposite angles )

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841