(Angles) Just 3 problems

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!