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1. The diagram shown is two intersecting lines. The measure of (5 is 47°.



(a) What is the measure of {7 ? How do you know. Explain your answer in complete sentences.

(b) Suppose the measure of {6 can be represented by (2x-5) . What equation can be written to solve for the value of x?

(c) What is the value of x?

1 The diagram shown is two intersecting lines The measure of 5 is 47a What is the measure of 7 How do you know Explain your answer in complete sentencesb Suppos class=

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By using what we know about intersecting lines, we will see that:

  • a) ∡7 = 47°
  • b) 47° + (2x - 5)° = 180°
  • c) x = 69

How to get the measures of the angles for two intersecting lines?

When two lines intersect, 4 angles are formed. There are two properties that these angles have.

  • If the angles are adjacent, then their measures add up to 180°
  • If the angles are not adjacent, these angles have the same measure.

a) We know that ∡5 = 47°

And 7 is not adjacent to 5, then 7 has the same measure:

∡7 = 47°

b) 6 and 5 are adjacent, then we must have that:

∡5 + ∡6 = 180°

47° + (2x - 5)° = 180°

That is the equation we need to solve to get the value of x.

c) To solve the linear equation we need to isolate x, let's do that:

47° + (2x - 5)° = 180°

(2x - 5)° = 180° - 47° = 133°

2x - 5 = 133

2x = 133 + 5 = 138

x = 138/2 = 69.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/1884491