Question

If Angle 1 has a measurement of 52 degrees, find the measurements of Angles 2-8. Show ALL work to receive full credit.

Angle 2 =
Angle 3 =
Angle 4 =
Angle 5 =
Angle 6 =
Angle 7 =
Angle 8 =

Answer 1

Answer:

Angle 1 =  52°

Angle 2 =  ∠1 = 52 °  (isosceles triangle)

Angle 3 =  180° - 2∠1 = 180° - 2(52°) = 76°

Angle 4 =  ∠3 = 76°  (vertical angles)

Angle 5 =  180° - 2∠4 = 180° - 2(76°) = 28°

Angle 6 =  ∠4 + ∠5 = 76° + 28° = 104° (exterior angle)

Angle 7 =  180° - 2(180° - 104°) = 180° - 2(76°) = 28°

Angle 8 = ∠6 = 104° (exterior angle)

Answer 2

Answer:

Step-by-step explanation:

Really nice problem

<1 = 52                         Given

<2= 52                         The triangle is isosceles. Angles are equal because they are opposite equal sides.

<3 = 180 - <1 - <2 = 180 - 2*52

<3= 180-104 = 76          Every triangle = 180 degrees.

<4 = 76                         Vertically opposite angles (which are equal)

<5 = 180 - 2*76 = 28    180 - 2 base angles (76)  taken away from 180

<6 = 76+28 = 104         The exterior angle equals <4 + <5

<7 = 180 - 2*Supplementary angle to <6     180 - 2*76 = 28

<8 = <7 + <4 = 28 + 76 = 104

See if you can figure out why I used angle 4