Math / Geometry

QuestionQuestion Watch Video Show
The measures of the angles of a triangle are shown in the figure below. Solve for x .

Studdy Solution

STEP 1

1. We are given a triangle.
2. One angle is $59^\circ$ .
3. The triangle is a right triangle, so one angle is $90^\circ$ .
4. We need to find the measure of the angle labeled $x^\circ$ .

STEP 2

1. Use the property of the sum of angles in a triangle.
2. Solve for the unknown angle $x$ .

STEP 3

Recall that the sum of the angles in any triangle is $180^\circ$ . In a right triangle, one of the angles is $90^\circ$ . Therefore, the sum of the other two angles must be:
$180^\circ - 90^\circ = 90^\circ$

STEP 4

We are given that one of the angles is $59^\circ$ . Let the unknown angle be $x^\circ$ . Therefore, the equation for the sum of the angles is:
$59^\circ + x^\circ = 90^\circ$

STEP 5

Solve for $x$ by subtracting $59^\circ$ from both sides of the equation:
$x^\circ = 90^\circ - 59^\circ$

STEP 6

Calculate the value:
$x^\circ = 31^\circ$
The measure of the angle labeled $x$ is:
$\boxed{31^\circ}$

Was this helpful?

QuestionQuestion Watch Video Show
The measures of the angles of a triangle are shown in the figure below. Solve for x .

Studdy Solution

STEP 1

1. We are given a triangle.
2. One angle is $59^\circ$ .
3. The triangle is a right triangle, so one angle is $90^\circ$ .
4. We need to find the measure of the angle labeled $x^\circ$ .

STEP 2

1. Use the property of the sum of angles in a triangle.
2. Solve for the unknown angle $x$ .

STEP 3

Recall that the sum of the angles in any triangle is $180^\circ$ . In a right triangle, one of the angles is $90^\circ$ . Therefore, the sum of the other two angles must be:
$180^\circ - 90^\circ = 90^\circ$

STEP 4

We are given that one of the angles is $59^\circ$ . Let the unknown angle be $x^\circ$ . Therefore, the equation for the sum of the angles is:
$59^\circ + x^\circ = 90^\circ$

STEP 5

Solve for $x$ by subtracting $59^\circ$ from both sides of the equation:
$x^\circ = 90^\circ - 59^\circ$

STEP 6

Calculate the value:
$x^\circ = 31^\circ$
The measure of the angle labeled $x$ is:
$\boxed{31^\circ}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionQuestion Watch Video ShowThe measures of the angles of a triangle are shown in the figure below. Solve for x .

Studdy Solution

STEP 1

1. We are given a triangle.2. One angle is 59∘ 59^\circ 59∘.3. The triangle is a right triangle, so one angle is 90∘ 90^\circ 90∘.4. We need to find the measure of the angle labeled x∘ x^\circ x∘.

STEP 2

1. Use the property of the sum of angles in a triangle.2. Solve for the unknown angle x x x.

STEP 3

Recall that the sum of the angles in any triangle is 180∘ 180^\circ 180∘. In a right triangle, one of the angles is 90∘ 90^\circ 90∘. Therefore, the sum of the other two angles must be:180∘−90∘=90∘ 180^\circ - 90^\circ = 90^\circ 180∘−90∘=90∘

STEP 4

We are given that one of the angles is 59∘ 59^\circ 59∘. Let the unknown angle be x∘ x^\circ x∘. Therefore, the equation for the sum of the angles is:59∘+x∘=90∘ 59^\circ + x^\circ = 90^\circ 59∘+x∘=90∘

STEP 5

Solve for x x x by subtracting 59∘ 59^\circ 59∘ from both sides of the equation:x∘=90∘−59∘ x^\circ = 90^\circ - 59^\circ x∘=90∘−59∘

STEP 6

Calculate the value:x∘=31∘ x^\circ = 31^\circ x∘=31∘ The measure of the angle labeled x x x is:31∘ \boxed{31^\circ} 31∘​

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionQuestion Watch Video Show
The measures of the angles of a triangle are shown in the figure below. Solve for x .

1. We are given a triangle.
2. One angle is $59^\circ$ .
3. The triangle is a right triangle, so one angle is $90^\circ$ .
4. We need to find the measure of the angle labeled $x^\circ$ .

1. Use the property of the sum of angles in a triangle.
2. Solve for the unknown angle $x$ .

Recall that the sum of the angles in any triangle is $180^\circ$ . In a right triangle, one of the angles is $90^\circ$ . Therefore, the sum of the other two angles must be:
$180^\circ - 90^\circ = 90^\circ$

We are given that one of the angles is $59^\circ$ . Let the unknown angle be $x^\circ$ . Therefore, the equation for the sum of the angles is:
$59^\circ + x^\circ = 90^\circ$

Solve for $x$ by subtracting $59^\circ$ from both sides of the equation:
$x^\circ = 90^\circ - 59^\circ$

Calculate the value:
$x^\circ = 31^\circ$
The measure of the angle labeled $x$ is:
$\boxed{31^\circ}$