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The sum of the measures of angles for a triangle is 180°. Find the value of x and then the measures of the 3 angles

dmitriy555 [2]

Answer:

The value of x is 50

The measures of the 3 angles are 50°, 100°, 30°

Step-by-step explanation:

Let us solve the question

∵ The sum of the measures of the angles of a triangle is 180°

∵ The measures of the 3 angles of the given Δ are x°, 2x°, (x - 20)°

→ Add them and equate the sum by 180

∴ x° + 2x° + (x - 20)° = 180°

→ Add the like terms

∵ (x + 2x + x) + (-20) = 180

∴ 4x - 20 = 180

→ Add 20 to both sides

∵ 4x - 20 + 20 = 180 + 20

∴ 4x = 200

→ Divide both sides by 4 to find x

∴ x = 50

∴ The value of x is 50

To find the measures of the 3 angles substitute x by 50 in their expressions

∵ The measure of one angle is x

∴ The measure of the 1st angle is 50°

∵ The measure of the 2nd angle is 2x

∴ The measure of the 2nd angle = 2(50)

∴ The measure of the 2nd angle is 100°

∵ The measure of the 3rd angle is (x - 20)

∴ The measure of the 3rd angle = (50 - 20)

∴ The measure of the 3rd angle is 30°

∴ The measures of the 3 angles are 50°, 100°, 30°

6 0

3 years ago

Find the arc length that subtends a central angle of 2 rad in a circle of radius 2mi

Vera_Pavlovna [14]

2 * 2 = 4 miles.
__________

8 0

3 years ago

Lydia is making spaghetti sauce at a community luncheon. Each batch requires 1⁄2 teaspoon of salt, 1⁄3 teaspoon of oregano, 1⁄4

Troyanec [42]

Salt is used in the largest quantity in Lydia's recipe.

Explanation

Required spices are......

Salt = $\frac{1}{2}$ teaspoon , Oregano = $\frac{1}{3}$ teaspoon, Crushed thyme = $\frac{1}{4}$ teaspoon and Black peeper = $\frac{1}{8}$ teaspoon

For finding the largest quantity, first we need to make the denominators of each fraction as equal and then identify the largest numerator.

The denominators are 2, 3, 4 and 8 and their LCM(Least common multiple) will be 24. So.....

$\frac{1}{2}= \frac{1*12}{2*12}=\frac{12}{24} \\ \\ \frac{1}{3}=\frac{1*8}{3*8}=\frac{8}{24}\\ \\ \frac{1}{4}=\frac{1*6}{4*6}=\frac{6}{24}\\ \\ \frac{1}{8}=\frac{1*3}{8*3}=\frac{3}{24}$

As the largest numerator is 12 here, so the value of $\frac{1}{2}$ is largest among all the fractions.

Thus, Salt is used in the largest quantity in Lydia's recipe.

5 0

3 years ago

(3,-3), slope 3 write an equation of the line that passes through the given point and has the given slope

tester [92]

Answer:

y = 3x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3, thus

y = 3x + c ← is the partial equation

To find c substitute (3, - 3) into the partial equation

- 3 = 9 + c ⇒ c = - 3 - 9 = - 12

y = 3x - 12 ← equation of line

4 0

4 years ago

Read 2 more answers

Brainly if it is correct

Musya8 [376]

Answer:

The third one

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers