Need , i do not understand. 11. find the values of x and y. (2 points) 12. find the measures of w, x, y and z. (3 points) 13. find the values for x and y. (4 points)

11. x=8, y=30

12. w=63°, x=86°, y=38°, z=25°

13. x=18, y=15

Step-by-step explanation:

You have been studying the angles related to transversals and parallel lines, so you know alternate (interior or exterior) angles are congruent (equal) and same-side (interior or exterior) angles are supplementary. You also know that linear angles sum to 180°, the measure of an angle formed by a straight line.

The red arrows in these diagrams signify that the lines so marked are parallel, so the above relationships apply.

11. The diagonal line is a transversal of the top and bottom parallel lines, so the angle marked 5x° is equal to the angle marked 40°. Writing that relationship as an equation, you have ...

... 5x° = 40° . . . . . . . the relationship of the angles

... x = 40/5 = 8 . . . . divide the equation by 5° to find x

The angle marked 3y° and the angle marked with a right-angle symbol are same-side interior angles formed by the vertical transversal with the top and bottom horizontal lines. Hence those angles are supplementary.

... 3y° +90° = 180°

... 3y° = 90° . . . . . . . subtract 90°

... y = 90/3 = 30 . . . .divide by 3°

12. These problems make use of the sum of angles that form a line (180°) and the sum of angles in a triangle (180°).

Together 117° and w form a line, so ...

... 117° + w = 180°

... w = 63° . . . . . . . . . . subtract 117°

The angles of a triangle add to give 180°, so ...

... w + 31° + x = 180°

... 63° +31° + x = 180° . . . . . put in the known value for w

... x = 180° -63° -31°

... x = 86°

Together, x and 56° and y form a line, so the sum of their measures is 180°.

... x + 56° + y = 180°

... 86° + 56° + y = 180° . . . . put in the known value for x

... y = 180° -86° -56° . . . . . . subtract the constants on the left

... y = 38°

The sum of angles y, 117°, and z is 180°.

... 38° + 117° + z = 180° . . . . use the known value for y

... z = 180° -38° -117° . . . . . . subtract the constants on the left

... z = 25°

13. The relationships used in problem 11 also can be used here.

... 5x° + 90° = 180°

... x = (180° -90°)/5°

... x = 18

The angles involving y are same-side interior angles, so are supplementary.

... 5(y +11)° + (4y -10)° = 180°

... 5y +55 + 4y -10 = 180 . . . . . . eliminate parentheses, divide by °

... 9y +45 = 180 . . . . . . . . . . . . . collect terms

... y + 5 = 20 . . . . . . . . . . . . . . . divide by 9

... y = 15 . . . . . . . . . . . . . . . . . . . .subtract 5

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?