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Anton [14]
3 years ago
8

Need Help, I do not understand.

Mathematics
1 answer:
Lady_Fox [76]3 years ago
8 0

Answer:

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

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jek_recluse [69]

Answer:

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Step-by-step explanation:

Law of cosines: The law of cosines is used for calculating one side of a triangle when the angle opposite and the other two sides are known.

If the information about a triangle according to SSS, SAS and ASA is given, then we will immediately use SSS and SAS  by using the law of cosines to find one of the remaining measures because Law of cosines is applied if we know one angle opposite and the other two sides.

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please mark me brainliest :)

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