Math / Geometry

Question $A B C$ гурвалжны $A$ оройг дайрсан шулуун $B C$ талыг $D$ цэгт огтолно. Хэрэв $\angle B A C=48^{\circ}$ ба $\measuredangle C A D=8^{\circ}$ бол $\measuredangle B A D$ өнцөг хэд байх вэ?

Studdy Solution

STEP 1

1. $\angle BAC$ is given as $48^\circ$ .
2. $\measuredangle CAD$ is given as $8^\circ$ .
3. We need to find $\measuredangle BAD$ .

STEP 2

1. Understand the relationship between the angles.
2. Use angle subtraction to find the desired angle.

STEP 3

Recognize that $\angle BAC$ is the entire angle at vertex $A$ formed by sides $AB$ and $AC$ .

STEP 4

Since $\measuredangle CAD$ is part of $\angle BAC$ , we can find $\measuredangle BAD$ by subtracting $\measuredangle CAD$ from $\angle BAC$ .

STEP 5

Calculate $\measuredangle BAD$ using the formula:
$\measuredangle BAD = \angle BAC - \measuredangle CAD$
Substitute the given values:
$\measuredangle BAD = 48^\circ - 8^\circ$

STEP 6

Perform the subtraction:
$\measuredangle BAD = 40^\circ$
The measure of $\measuredangle BAD$ is:
$\boxed{40^\circ}$

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Question $A B C$ гурвалжны $A$ оройг дайрсан шулуун $B C$ талыг $D$ цэгт огтолно. Хэрэв $\angle B A C=48^{\circ}$ ба $\measuredangle C A D=8^{\circ}$ бол $\measuredangle B A D$ өнцөг хэд байх вэ?

Studdy Solution

STEP 1

1. $\angle BAC$ is given as $48^\circ$ .
2. $\measuredangle CAD$ is given as $8^\circ$ .
3. We need to find $\measuredangle BAD$ .

STEP 2

1. Understand the relationship between the angles.
2. Use angle subtraction to find the desired angle.

STEP 3

Recognize that $\angle BAC$ is the entire angle at vertex $A$ formed by sides $AB$ and $AC$ .

STEP 4

Since $\measuredangle CAD$ is part of $\angle BAC$ , we can find $\measuredangle BAD$ by subtracting $\measuredangle CAD$ from $\angle BAC$ .

STEP 5

Calculate $\measuredangle BAD$ using the formula:
$\measuredangle BAD = \angle BAC - \measuredangle CAD$
Substitute the given values:
$\measuredangle BAD = 48^\circ - 8^\circ$

STEP 6

Perform the subtraction:
$\measuredangle BAD = 40^\circ$
The measure of $\measuredangle BAD$ is:
$\boxed{40^\circ}$

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Studdy Solution

STEP 1

1. ∠BAC \angle BAC ∠BAC is given as 48∘ 48^\circ 48∘.2. ∡CAD \measuredangle CAD ∡CAD is given as 8∘ 8^\circ 8∘.3. We need to find ∡BAD \measuredangle BAD ∡BAD.

STEP 2

1. Understand the relationship between the angles.2. Use angle subtraction to find the desired angle.

STEP 3

Recognize that ∠BAC \angle BAC ∠BAC is the entire angle at vertex A A A formed by sides AB AB AB and AC AC AC.

STEP 4

Since ∡CAD \measuredangle CAD ∡CAD is part of ∠BAC \angle BAC ∠BAC, we can find ∡BAD \measuredangle BAD ∡BAD by subtracting ∡CAD \measuredangle CAD ∡CAD from ∠BAC \angle BAC ∠BAC.

STEP 5

Calculate ∡BAD \measuredangle BAD ∡BAD using the formula:∡BAD=∠BAC−∡CAD \measuredangle BAD = \angle BAC - \measuredangle CAD ∡BAD=∠BAC−∡CADSubstitute the given values:∡BAD=48∘−8∘ \measuredangle BAD = 48^\circ - 8^\circ ∡BAD=48∘−8∘

STEP 6

Perform the subtraction:∡BAD=40∘ \measuredangle BAD = 40^\circ ∡BAD=40∘ The measure of ∡BAD \measuredangle BAD ∡BAD is:40∘ \boxed{40^\circ} 40∘​

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1. $\angle BAC$ is given as $48^\circ$ .
2. $\measuredangle CAD$ is given as $8^\circ$ .
3. We need to find $\measuredangle BAD$ .

1. Understand the relationship between the angles.
2. Use angle subtraction to find the desired angle.

Recognize that $\angle BAC$ is the entire angle at vertex $A$ formed by sides $AB$ and $AC$ .

Since $\measuredangle CAD$ is part of $\angle BAC$ , we can find $\measuredangle BAD$ by subtracting $\measuredangle CAD$ from $\angle BAC$ .

Calculate $\measuredangle BAD$ using the formula:
$\measuredangle BAD = \angle BAC - \measuredangle CAD$
Substitute the given values:
$\measuredangle BAD = 48^\circ - 8^\circ$

Perform the subtraction:
$\measuredangle BAD = 40^\circ$
The measure of $\measuredangle BAD$ is:
$\boxed{40^\circ}$