First attachment:
Angle Q and Angle S measure 61°
Second attachment:
Angle A measures 60°
Angle B and Angle D are congruent and measure 90°
Angle C measures 39°
Angle E measures 51°
Third attachment:
a. 3x+51=180, x=43
b. Angle 1 measures 129° and Angle 2 measures 51°
Step-by-step explanation:
First attachment:
If a triangle measures 180°, then you can subtract 58 from 180, then divide the answer by 2 to figure out the degree measure of Angle Q and Angle S because they both have the same measure.
180-58=122
122/2=61°
Second attachment:
Angle A has an angle to the right that measures 125°. If a straight angle measures 180°, then you can subtract 125 from 180 to find the measure of Angle A (60°).
Angle B and Angle D are opposite interior angles, so they are congruent. After finding the measure of Angle E, we can subtract the measure of Angle E and the third angle of the triangle (that is shown to measure 39°) from 180° to determine the measure of Angle D and Angle B. (You can do the same method to Triangle ABC to find the measure of angle B). After determining that Angle E measures 51°, you can determine that Angles B and D measure 90°.
Angle C measures 39° because Angle C and the angle that measures 39° are vertical angles, and therefore, are congruent.
Angle E has an angle to the right that measures 129°. If a straight angle measures 180°, then you can subtract 129 from 180 to find the measure of Angle E (51°).
Third attachment:
If the two angles are supplementary, then they add up to 180°.
a. Taking that into consideration, 3x (Angle 1) + 51 (Angle 2) = 180°
To solve for x, subtract 51 from both sides
3x+51=180°
-51 -51
3x=129
Then divide 3x from both sides
3x/3=129/3
x=43
b. Angle 2 (51°) is already given, but you need to find out the measure of Angle 1. To find the measure of Angle 1, plug your x value into 3x.
3(43)=129°
Angle 1 = 129°
Hope This Helps!
