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18 votes
18 votes
4. The three lines shown in the diagram below intersect at the same point. The measures of some of the angles in degrees are given as 2(-2 + y), 5xº, 36° and 20°. a. Write and solve an equation that can be used to find the value of y. Hint: Use your knowledge of vertical angles.

4. The three lines shown in the diagram below intersect at the same point. The measures-example-1
User Bjedrzejewski
by
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1 Answer

18 votes
18 votes

Part A. Write and solve an equation that can be used to find the value of y.

Given: (Using the principles of vertical angles.)

Solution:

Equation: 2(-2 + y) = 20


\begin{gathered} 2(-2+y)=20 \\ -4+2y=20 \\ 2y=20+4 \\ 2y=24 \\ (2y)/(2)=(24)/(2) \\ y=12 \end{gathered}

Part B. Write and solve an equation that can be used to find the value of x.

Given: (Using the sum of the angles of a straight line.)

Note: The sum of the angles of a straight line is equal to 180 degrees.

Solution:

Equation: 5x + 36 + 20 = 180


\begin{gathered} 5x+36+20=180 \\ 5x+56=180 \\ 5x=180-56 \\ 5x=124 \\ (5x)/(5)=(124)/(5) \\ x=24.8 \end{gathered}

ANSWERS:

Part A: 2(-2 +y) = 20, y = 12

Part B: 5x + 36 + 20 = 180, x = 24.8

4. The three lines shown in the diagram below intersect at the same point. The measures-example-1
4. The three lines shown in the diagram below intersect at the same point. The measures-example-2
User Alex Logan
by
2.7k points
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