3. If m angle 2=98°, m angle 3=23°, and m angle 8=70°, find each measure. 4. If m angle 3=54°, find each measure.

The measure of an an angle can be found from other known angles and the angular relationships present

The measures of the angles are;

3. a. m∠1 = 82°,         b. m∠4 = 59°,        c. m∠5 = 98°,      d. m∠6 = 51°,            e. m∠7 = 59°,              f. m∠9 = 51°

4. a. m∠1 = 36°,       b. m∠2 = 90°,       c. m∠4 = 36°,          d. m∠5 = 90°,                      e. m∠6 = 54°,          f. m∠7 = 126°,       g. m∠8 = 54°,         h. m∠9 = 126°,          i. m∠10 = 54°,          j. m∠11 = 36°,         k. m∠12 = 144°,      l. m∠13 = 36°,         m. m∠14 = 144°

The reason the above values are correct are as follows;

The known parameters are;

m∠2 = 98°

m∠3 = 23°

m∠8 = 70°

a. m∠1 and m∠2 are linear pair angles

Therefore;

m∠1 + m∠2 = 180°

m∠1  + 98° = 180°

m∠1 = 180° - 98° = 82°

m∠1 = 82°

b. m∠4 = m∠7 = 180° - m∠2 - m∠3

∴ m∠4 = 180° - 98° - 23° = 59°

m∠4 = 59°

c. m∠5 = 180° - m∠3 - m∠4 (sum of angles on a line)

∴ m∠5 = 180° - 23° - 59° = 98°

m∠5 = 98°

Also m∠2 = m∠5 (corresponding angles)

d. m∠6 = 180 - m∠7 - m∠8 (sum of angles on a line)

∴ m∠6 = 180° - 59° - 70° = 51°

m∠6 = 51°

e. m∠7 = m∠4 = 59° (alternate interior angles theorem)

f. m∠9 = 180 - m∠4 - m∠8 (angles sum property of a triangle)

∴ m∠9 = 180° - 59° - 70° = 51°

m∠9 = 51°

Also, m∠9 = m∠6 = 51° (corresponding angles)

4. m∠3 = 54° (given)

a. m∠1 = 180° - 90° - 54° = 36° (sum of angles on a line)

m∠1 = 36°

b. m∠2 = 90° (given, geometry symbol)

c. m∠4 = m∠1 = 36° (vertical angles)

m∠4 = 36°

d. m∠5 = m∠2 = 90° (vertical angles)

m∠5 = 90°

e. m∠6 = m∠3 = 54° (vertical angles)

m∠6 = 54°

f. m∠7 = m∠1 + m∠2 (corresponding angles, angle addition)

m∠7 = 36° + 90° = 126°

m∠7 = 126°

g. m∠8 = 180° - m∠7 (linear pair)

m∠8 = 180° - 126° = 54°

m∠8 = 54°

h. m∠9 = m∠7 = 126° (vertical angles)

m∠9 = 126°

i. m∠10 = m∠8 = 54° (vertical angles)

m∠10 = 54°

j. m∠11 = 180° - m∠5 - m∠8 (angles sum property of a triangle)

m∠11 = 180° - 90° - 54° = 36°

m∠11 = 36°

k. m∠12 = 180° - m∠11 (linear pair)

m∠12 = 180° - 36° = 144°

m∠12 = 144°

l. m∠13 = m∠11 = 36° (vertical angles)

m∠13 = 36°

m. m∠14 = m∠12 = 144° (vertical angles)

m∠14 = 144°

Learn more about angles formed between two parallel lines having a common transversal here:

link

Step-by-step explanation:

3). m∠1 = 180° - 98° = 82°

m∠7 = 180° - ( 98° + 23° ) = 59°

m∠6 = 180° - ( 70° + 59° ) = 51°

m∠9 = m∠6 = 51°

m∠10 = 180° - 51° = 129°

m∠4 = 180° - ( 70° + 51° ) = 59°

m∠54 = 180° - (23° + 59° ) = 98°

4). m∠1 = m∠4 = m∠11 = m∠13 = 90° - 54° = 36°

m∠2 = m∠5 = 90°

m∠6 = m∠3 = m∠8 = m∠10 = 54°

m∠7 = m∠9 = 90° + 36° = 126°

m∠12 = m∠14 = 180° - 36° = 144°

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

21

jk it's 20

step-by-step explanation: