Math / Geometry

QuestionXII. Харьцаа, пропори
19. Гурвалжны дотоод онцгҮүд $3: 5: 4$ харьцаатай бол тус бүрийн хәмжәэг ол

Studdy Solution

STEP 1

1. We are given a triangle.
2. The ratio of the interior angles is $3:5:4$ .
3. The sum of the interior angles of a triangle is $180^\circ$ .
4. We need to find the measure of each angle.

STEP 2

1. Set up an equation using the given ratio.
2. Solve the equation to find the value of each angle.
3. Verify that the sum of the angles is $180^\circ$ .

STEP 3

Let the measures of the angles be $3x$ , $5x$ , and $4x$ based on the given ratio $3:5:4$ . The sum of the angles in a triangle is $180^\circ$ . Therefore, we can write the equation:
$3x + 5x + 4x = 180$

STEP 4

Combine the terms in the equation:
$12x = 180$
Now, solve for $x$ :
$x = \frac{180}{12}$ $x = 15$

STEP 5

Substitute $x = 15$ back into the expressions for each angle:
First angle: $3x = 3 \times 15 = 45^\circ$
Second angle: $5x = 5 \times 15 = 75^\circ$
Third angle: $4x = 4 \times 15 = 60^\circ$

STEP 6

Verify that the sum of the angles is $180^\circ$ :
$45^\circ + 75^\circ + 60^\circ = 180^\circ$
The calculation is correct.
The measures of the angles are $45^\circ$ , $75^\circ$ , and $60^\circ$ .

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QuestionXII. Харьцаа, пропори
19. Гурвалжны дотоод онцгҮүд $3: 5: 4$ харьцаатай бол тус бүрийн хәмжәэг ол

Studdy Solution

STEP 1

1. We are given a triangle.
2. The ratio of the interior angles is $3:5:4$ .
3. The sum of the interior angles of a triangle is $180^\circ$ .
4. We need to find the measure of each angle.

STEP 2

1. Set up an equation using the given ratio.
2. Solve the equation to find the value of each angle.
3. Verify that the sum of the angles is $180^\circ$ .

STEP 3

Let the measures of the angles be $3x$ , $5x$ , and $4x$ based on the given ratio $3:5:4$ . The sum of the angles in a triangle is $180^\circ$ . Therefore, we can write the equation:
$3x + 5x + 4x = 180$

STEP 4

Combine the terms in the equation:
$12x = 180$
Now, solve for $x$ :
$x = \frac{180}{12}$ $x = 15$

STEP 5

Substitute $x = 15$ back into the expressions for each angle:
First angle: $3x = 3 \times 15 = 45^\circ$
Second angle: $5x = 5 \times 15 = 75^\circ$
Third angle: $4x = 4 \times 15 = 60^\circ$

STEP 6

Verify that the sum of the angles is $180^\circ$ :
$45^\circ + 75^\circ + 60^\circ = 180^\circ$
The calculation is correct.
The measures of the angles are $45^\circ$ , $75^\circ$ , and $60^\circ$ .

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QuestionXII. Харьцаа, пропори19. Гурвалжны дотоод онцгҮүд 3:5:43: 5: 43:5:4 харьцаатай бол тус бүрийн хәмжәэг ол

Studdy Solution

STEP 1

1. We are given a triangle.2. The ratio of the interior angles is 3:5:43:5:43:5:4.3. The sum of the interior angles of a triangle is 180∘180^\circ180∘.4. We need to find the measure of each angle.

STEP 2

1. Set up an equation using the given ratio.2. Solve the equation to find the value of each angle.3. Verify that the sum of the angles is 180∘180^\circ180∘.

STEP 3

Let the measures of the angles be 3x3x3x, 5x5x5x, and 4x4x4x based on the given ratio 3:5:43:5:43:5:4. The sum of the angles in a triangle is 180∘180^\circ180∘. Therefore, we can write the equation:3x+5x+4x=180 3x + 5x + 4x = 180 3x+5x+4x=180

STEP 4

Combine the terms in the equation:12x=180 12x = 180 12x=180Now, solve for xxx:x=18012 x = \frac{180}{12} x=12180​ x=15 x = 15 x=15

STEP 5

Substitute x=15x = 15x=15 back into the expressions for each angle:First angle: 3x=3×15=45∘3x = 3 \times 15 = 45^\circ3x=3×15=45∘Second angle: 5x=5×15=75∘5x = 5 \times 15 = 75^\circ5x=5×15=75∘Third angle: 4x=4×15=60∘4x = 4 \times 15 = 60^\circ4x=4×15=60∘

STEP 6

Verify that the sum of the angles is 180∘180^\circ180∘:45∘+75∘+60∘=180∘ 45^\circ + 75^\circ + 60^\circ = 180^\circ 45∘+75∘+60∘=180∘The calculation is correct. The measures of the angles are 45∘45^\circ45∘, 75∘75^\circ75∘, and 60∘60^\circ60∘.

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QuestionXII. Харьцаа, пропори
19. Гурвалжны дотоод онцгҮүд $3: 5: 4$ харьцаатай бол тус бүрийн хәмжәэг ол

1. We are given a triangle.
2. The ratio of the interior angles is $3:5:4$ .
3. The sum of the interior angles of a triangle is $180^\circ$ .
4. We need to find the measure of each angle.

1. Set up an equation using the given ratio.
2. Solve the equation to find the value of each angle.
3. Verify that the sum of the angles is $180^\circ$ .

Let the measures of the angles be $3x$ , $5x$ , and $4x$ based on the given ratio $3:5:4$ . The sum of the angles in a triangle is $180^\circ$ . Therefore, we can write the equation:
$3x + 5x + 4x = 180$

Combine the terms in the equation:
$12x = 180$
Now, solve for $x$ :
$x = \frac{180}{12}$ $x = 15$

Substitute $x = 15$ back into the expressions for each angle:
First angle: $3x = 3 \times 15 = 45^\circ$
Second angle: $5x = 5 \times 15 = 75^\circ$
Third angle: $4x = 4 \times 15 = 60^\circ$

Verify that the sum of the angles is $180^\circ$ :
$45^\circ + 75^\circ + 60^\circ = 180^\circ$
The calculation is correct.
The measures of the angles are $45^\circ$ , $75^\circ$ , and $60^\circ$ .