The ratio of the measures of the angle in a triangle is 4: 10: 6. find the measures of the smallest angles

36° and 54°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the parts of the ratio,  4 + 10 + 6 = 20 parts

Divide 180 by 20 to find the value of one part of the ratio

180° ÷20 = 9° ← value of 1 part of the ratio

4 parts = 4 × 9° = 36°

10 parts = 10 × 9° = 90°

6 parts = 6 × 9° = 54°

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