Question

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 (2 5 x − ) . What equation can be written to solve for the value of x? (c) What is the value of x?

Answer 1

a) <5 and <7 have congruent angles. That means that both angles are equal, they have the same measure. This means that the measure of <7 is 47°.

<7 = 47°

b) 5 and 6 are adjacent, so this is the equation that we have to do to solve for the value of x.

<5 + <6 = 180°

47° + (2x - 5)° = 180°

c) To solve the linear equation we need to isolate x.

47° + (2x - 5)° = 180°

(2x - 5)° = 180° - 47° = 133°

2x - 5 = 133

2x = 133 + 5 = 138

x = 138/2 = 69

Answer 2

the measure of 7 is 47 degrees, the equation is 2x -5 + 47 = 180 and the value of x is = to 69

Explanation: