Math / Geometry

QuestionFind the measures of the intertor angles of the triangle. $\angle A=$ $\square$ $\angle B=$ $\square$ $\angle C=$ $\square$

Studdy Solution

STEP 1

1. We are given a triangle $\triangle ABC$ .
2. Angle $A$ is $30^\circ$ .
3. Angle $C$ is a right angle, $90^\circ$ .
4. Angle $B$ is labeled as $x$ .
5. The sum of the interior angles of a triangle is $180^\circ$ .

STEP 2

1. Use the property of the sum of interior angles of a triangle.
2. Calculate the measure of angle $B$ .

STEP 3

The sum of the interior angles of a triangle is always $180^\circ$ . Therefore, we can write the equation:
$\angle A + \angle B + \angle C = 180^\circ$

STEP 4

Substitute the known values into the equation. We know $\angle A = 30^\circ$ and $\angle C = 90^\circ$ :
$30^\circ + x + 90^\circ = 180^\circ$

STEP 5

Solve for $x$ (which is $\angle B$ ):
$30^\circ + 90^\circ + x = 180^\circ$ $120^\circ + x = 180^\circ$ $x = 180^\circ - 120^\circ$ $x = 60^\circ$
The measures of the interior angles of the triangle are:
$\angle A = 30^\circ$ $\angle B = 60^\circ$ $\angle C = 90^\circ$

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QuestionFind the measures of the intertor angles of the triangle. $\angle A=$ $\square$ $\angle B=$ $\square$ $\angle C=$ $\square$

Studdy Solution

STEP 1

1. We are given a triangle $\triangle ABC$ .
2. Angle $A$ is $30^\circ$ .
3. Angle $C$ is a right angle, $90^\circ$ .
4. Angle $B$ is labeled as $x$ .
5. The sum of the interior angles of a triangle is $180^\circ$ .

STEP 2

1. Use the property of the sum of interior angles of a triangle.
2. Calculate the measure of angle $B$ .

STEP 3

The sum of the interior angles of a triangle is always $180^\circ$ . Therefore, we can write the equation:
$\angle A + \angle B + \angle C = 180^\circ$

STEP 4

Substitute the known values into the equation. We know $\angle A = 30^\circ$ and $\angle C = 90^\circ$ :
$30^\circ + x + 90^\circ = 180^\circ$

STEP 5

Solve for $x$ (which is $\angle B$ ):
$30^\circ + 90^\circ + x = 180^\circ$ $120^\circ + x = 180^\circ$ $x = 180^\circ - 120^\circ$ $x = 60^\circ$
The measures of the interior angles of the triangle are:
$\angle A = 30^\circ$ $\angle B = 60^\circ$ $\angle C = 90^\circ$

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QuestionFind the measures of the intertor angles of the triangle. ∠A=\angle A=∠A= □\square□ ∠B=\angle B=∠B= □\square□ ∠C=\angle C=∠C= □\square□

Studdy Solution

STEP 1

1. We are given a triangle △ABC \triangle ABC △ABC.2. Angle A A A is 30∘ 30^\circ 30∘.3. Angle C C C is a right angle, 90∘ 90^\circ 90∘.4. Angle B B B is labeled as x x x.5. The sum of the interior angles of a triangle is 180∘ 180^\circ 180∘.

STEP 2

1. Use the property of the sum of interior angles of a triangle.2. Calculate the measure of angle B B B.

STEP 3

The sum of the interior angles of a triangle is always 180∘ 180^\circ 180∘. Therefore, we can write the equation:∠A+∠B+∠C=180∘ \angle A + \angle B + \angle C = 180^\circ ∠A+∠B+∠C=180∘

STEP 4

Substitute the known values into the equation. We know ∠A=30∘ \angle A = 30^\circ ∠A=30∘ and ∠C=90∘ \angle C = 90^\circ ∠C=90∘:30∘+x+90∘=180∘ 30^\circ + x + 90^\circ = 180^\circ 30∘+x+90∘=180∘

STEP 5

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QuestionFind the measures of the intertor angles of the triangle. $\angle A=$ $\square$ $\angle B=$ $\square$ $\angle C=$ $\square$

1. We are given a triangle $\triangle ABC$ .
2. Angle $A$ is $30^\circ$ .
3. Angle $C$ is a right angle, $90^\circ$ .
4. Angle $B$ is labeled as $x$ .
5. The sum of the interior angles of a triangle is $180^\circ$ .

1. Use the property of the sum of interior angles of a triangle.
2. Calculate the measure of angle $B$ .

The sum of the interior angles of a triangle is always $180^\circ$ . Therefore, we can write the equation:
$\angle A + \angle B + \angle C = 180^\circ$

Substitute the known values into the equation. We know $\angle A = 30^\circ$ and $\angle C = 90^\circ$ :
$30^\circ + x + 90^\circ = 180^\circ$