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I need help 7 th grade math

I need help 7 th grade math-example-1

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Answer:

See each problem below.

Explanation:

1. The 3 streets, North, Center, and South are parallel.

Avenue A is perpendicular to North Street.

That means the angles formed by North Street and Avenue A are right angles. Because of corresponding angles and parallel lines, the angles formed by Avenue A with Center Street and also the angles formed by Avenue A and South Street are also all right angles. That makes those corresponding angles congruent. That makes Avenue A and South Street perpendicular.

2. One angle is corresponding to the 70° angle and also measures 70°. The adjacent angle to the 70° angle is supplementary to it and measures 110°.

70°, 100°

3. Angles ACB and ACD form a linear pair and are supplementary. That means that the sum of their measures is 180°.

m<ACB + m<ACD = 180°

5x + m<ACD = 180

m<ACD = 180 - 5x

4. Angles BCF and CFE are same side interior angles of parallel lines cut by a transversal, so they are supplementary.

m<BCF + m<CFE = 180°

4x + 11x = 180

15x = 180

x = 12

m<BCF = 4x = 4(12) = 48

m<CFE = 11x = 11(12) = 132

m<BCF = 48°

m<CFE = 132°

5.

Angles CFG and DCF are same side interior angles of parallel lines cut by a transversal, so they are supplementary.

m<BCF + m<CFE = 180°

(3x) + (7x + 40) = 180

10x = 140

x = 14

m<CFG = 3x = 3(14) = 42

m<DCF = 7x + 40 = 7(14) + 40 = 138

m<CFG = 42°

m<DCF = 138°

6. See picture below.

7. <AGE, <BEG, <CHG, <DHF

8. If m<AGE = 85°, what is m<CHG?

Answer: Angles AGE and CHG are corresponding angles, so they are congruent.

m<CHG = 85°

I need help 7 th grade math-example-1
User RonyHe
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