Math / Geometry

Question $x^{\circ}$ $124^{\circ}$ Side of the triangle below has been extended to form an exterior angle of $124^{\circ}$ . Find the value of $x$ .

Studdy Solution

STEP 1

What is this asking? We need to find the value of an angle inside a right triangle, given an exterior angle. Watch out! Don't forget that a right angle measures $90^\circ$ !

STEP 2

1. Find the adjacent angle
2. Find $x$

STEP 3

A straight line forms an angle of $180^\circ$ .
The exterior angle of $124^\circ$ and the adjacent angle inside the triangle must add up to $180^\circ$ .

STEP 4

Let's call the adjacent angle $a$ .
We know that $a + 124^\circ = 180^\circ$ .
To find $a$ , we subtract $124^\circ$ from both sides: $a = 180^\circ - 124^\circ = \mathbf{56^\circ}$ So, the adjacent angle is $\mathbf{56^\circ}$ .

STEP 5

The sum of the angles in any triangle is $180^\circ$ .
We have a right triangle, so one angle is $90^\circ$ , another is $\mathbf{56^\circ}$ (from the previous step), and the last angle is $x$ .

STEP 6

We know that $90^\circ + 56^\circ + x = 180^\circ$ .
First, let's combine the known angles: $146^\circ + x = 180^\circ$ Now, we subtract $146^\circ$ from both sides of the equation: $x = 180^\circ - 146^\circ = \mathbf{34^\circ}$ So, $x = \mathbf{34^\circ}$ !

STEP 7

The value of $x$ is $\mathbf{34^\circ}$ .

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Question $x^{\circ}$ $124^{\circ}$ Side of the triangle below has been extended to form an exterior angle of $124^{\circ}$ . Find the value of $x$ .

Studdy Solution

STEP 1

What is this asking? We need to find the value of an angle inside a right triangle, given an exterior angle. Watch out! Don't forget that a right angle measures $90^\circ$ !

STEP 2

1. Find the adjacent angle
2. Find $x$

STEP 3

A straight line forms an angle of $180^\circ$ .
The exterior angle of $124^\circ$ and the adjacent angle inside the triangle must add up to $180^\circ$ .

STEP 4

Let's call the adjacent angle $a$ .
We know that $a + 124^\circ = 180^\circ$ .
To find $a$ , we subtract $124^\circ$ from both sides: $a = 180^\circ - 124^\circ = \mathbf{56^\circ}$ So, the adjacent angle is $\mathbf{56^\circ}$ .

STEP 5

The sum of the angles in any triangle is $180^\circ$ .
We have a right triangle, so one angle is $90^\circ$ , another is $\mathbf{56^\circ}$ (from the previous step), and the last angle is $x$ .

STEP 6

We know that $90^\circ + 56^\circ + x = 180^\circ$ .
First, let's combine the known angles: $146^\circ + x = 180^\circ$ Now, we subtract $146^\circ$ from both sides of the equation: $x = 180^\circ - 146^\circ = \mathbf{34^\circ}$ So, $x = \mathbf{34^\circ}$ !

STEP 7

The value of $x$ is $\mathbf{34^\circ}$ .

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Questionx∘x^{\circ}x∘ 124∘124^{\circ}124∘ Side of the triangle below has been extended to form an exterior angle of 124∘124^{\circ}124∘. Find the value of xxx.

Studdy Solution

STEP 1

What is this asking? We need to find the value of an angle inside a right triangle, given an exterior angle. Watch out! Don't forget that a right angle measures 90∘90^\circ90∘!

STEP 2

1. Find the adjacent angle2. Find xxx

STEP 3

A straight line forms an angle of 180∘180^\circ180∘.The exterior angle of 124∘124^\circ124∘ and the adjacent angle inside the triangle must add up to 180∘180^\circ180∘.

STEP 4

STEP 5

The sum of the angles in *any* triangle is 180∘180^\circ180∘.We have a right triangle, so one angle is 90∘90^\circ90∘, another is 56∘\mathbf{56^\circ}56∘ (from the previous step), and the last angle is xxx.

STEP 6

STEP 7

The value of xxx is 34∘\mathbf{34^\circ}34∘.

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Studdy solves anything!

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

Question $x^{\circ}$ $124^{\circ}$ Side of the triangle below has been extended to form an exterior angle of $124^{\circ}$ . Find the value of $x$ .

What is this asking? We need to find the value of an angle inside a right triangle, given an exterior angle. Watch out! Don't forget that a right angle measures $90^\circ$ !

1. Find the adjacent angle
2. Find $x$

A straight line forms an angle of $180^\circ$ .
The exterior angle of $124^\circ$ and the adjacent angle inside the triangle must add up to $180^\circ$ .

The sum of the angles in any triangle is $180^\circ$ .
We have a right triangle, so one angle is $90^\circ$ , another is $\mathbf{56^\circ}$ (from the previous step), and the last angle is $x$ .

The value of $x$ is $\mathbf{34^\circ}$ .