Find the measure of angle abc. a. 124 b. 97 c. 56 d. 51

Answer D. 51

Step-by-step explanation:

Sum of the interior angles of a triangle is up to 180

.: 32+(2x-15) + (x-5) = 180

Group like terms

2x+x =180 - 32 + 15 + 5

When - and + sign cross equal sign it turns to the opposite

3x = 168

x= 168/3

.: X =56

Now put x = 56 in (x - 5)

Angle ABC = 51

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

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