Math / Geometry

QuestionDalam Rajah 2, ABCDEFGH ialah sebuah oktagon sekata. Diberi bahawa HI dan GF ialah garis selari.
Cari nilai $p$ .
A $131^{\circ}$
B $136^{\circ}$
C $151^{\circ}$
D $209^{\circ}$

Studdy Solution

STEP 1

1. ABCDEFGH is a regular octagon.
2. The sum of the interior angles of a polygon with $n$ sides is given by $(n-2) \times 180^\circ$ .
3. HI and GF are parallel lines.
4. We are tasked with finding the value of $p$ .

STEP 2

1. Calculate the interior angle of a regular octagon.
2. Use the properties of parallel lines and angles to find $p$ .

STEP 3

Calculate the sum of the interior angles of the octagon using the formula:
$\text{Sum of interior angles} = (n-2) \times 180^\circ$
where $n = 8$ for an octagon.

STEP 4

Substitute $n = 8$ into the formula:
$\text{Sum of interior angles} = (8-2) \times 180^\circ$ $= 6 \times 180^\circ$ $= 1080^\circ$

STEP 5

Since the octagon is regular, each interior angle is equal. Divide the sum of the interior angles by 8:
$\text{Each interior angle} = \frac{1080^\circ}{8}$ $= 135^\circ$

STEP 6

Since HI and GF are parallel, and given that ∠HAB = 75° and ∠FGH = 286°, use the properties of parallel lines to find the angle ∠J, which is marked as $p$ .

STEP 7

Identify the relationship between the angles. Since HI and GF are parallel, the exterior angle ∠FGH and the interior angle ∠J (which is $p$ ) are supplementary because they form a straight line:
$\text{∠J} + \text{∠FGH} = 360^\circ$

STEP 8

Substitute ∠FGH = 286° into the equation:
$p + 286^\circ = 360^\circ$

STEP 9

Solve for $p$ :
$p = 360^\circ - 286^\circ$ $p = 74^\circ$
The value of $p$ is:
$\boxed{74^\circ}$

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QuestionDalam Rajah 2, ABCDEFGH ialah sebuah oktagon sekata. Diberi bahawa HI dan GF ialah garis selari.
Cari nilai $p$ .
A $131^{\circ}$
B $136^{\circ}$
C $151^{\circ}$
D $209^{\circ}$

Studdy Solution

STEP 1

1. ABCDEFGH is a regular octagon.
2. The sum of the interior angles of a polygon with $n$ sides is given by $(n-2) \times 180^\circ$ .
3. HI and GF are parallel lines.
4. We are tasked with finding the value of $p$ .

STEP 2

1. Calculate the interior angle of a regular octagon.
2. Use the properties of parallel lines and angles to find $p$ .

STEP 3

Calculate the sum of the interior angles of the octagon using the formula:
$\text{Sum of interior angles} = (n-2) \times 180^\circ$
where $n = 8$ for an octagon.

STEP 4

Substitute $n = 8$ into the formula:
$\text{Sum of interior angles} = (8-2) \times 180^\circ$ $= 6 \times 180^\circ$ $= 1080^\circ$

STEP 5

Since the octagon is regular, each interior angle is equal. Divide the sum of the interior angles by 8:
$\text{Each interior angle} = \frac{1080^\circ}{8}$ $= 135^\circ$

STEP 6

Since HI and GF are parallel, and given that ∠HAB = 75° and ∠FGH = 286°, use the properties of parallel lines to find the angle ∠J, which is marked as $p$ .

STEP 7

Identify the relationship between the angles. Since HI and GF are parallel, the exterior angle ∠FGH and the interior angle ∠J (which is $p$ ) are supplementary because they form a straight line:
$\text{∠J} + \text{∠FGH} = 360^\circ$

STEP 8

Substitute ∠FGH = 286° into the equation:
$p + 286^\circ = 360^\circ$

STEP 9

Solve for $p$ :
$p = 360^\circ - 286^\circ$ $p = 74^\circ$
The value of $p$ is:
$\boxed{74^\circ}$

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QuestionDalam Rajah 2, ABCDEFGH ialah sebuah oktagon sekata. Diberi bahawa HI dan GF ialah garis selari.Cari nilai p p p.A 131∘ 131^{\circ} 131∘B 136∘ 136^{\circ} 136∘C 151∘ 151^{\circ} 151∘D 209∘ 209^{\circ} 209∘

Studdy Solution

STEP 1

1. ABCDEFGH is a regular octagon.2. The sum of the interior angles of a polygon with n n n sides is given by (n−2)×180∘ (n-2) \times 180^\circ (n−2)×180∘.3. HI and GF are parallel lines.4. We are tasked with finding the value of p p p.

STEP 2

1. Calculate the interior angle of a regular octagon.2. Use the properties of parallel lines and angles to find p p p.

STEP 3

Calculate the sum of the interior angles of the octagon using the formula:Sum of interior angles=(n−2)×180∘ \text{Sum of interior angles} = (n-2) \times 180^\circ Sum of interior angles=(n−2)×180∘where n=8 n = 8 n=8 for an octagon.

STEP 4

Substitute n=8 n = 8 n=8 into the formula:Sum of interior angles=(8−2)×180∘ \text{Sum of interior angles} = (8-2) \times 180^\circ Sum of interior angles=(8−2)×180∘ =6×180∘ = 6 \times 180^\circ =6×180∘ =1080∘ = 1080^\circ =1080∘

STEP 5

Since the octagon is regular, each interior angle is equal. Divide the sum of the interior angles by 8:Each interior angle=1080∘8 \text{Each interior angle} = \frac{1080^\circ}{8} Each interior angle=81080∘​ =135∘ = 135^\circ =135∘

STEP 6

Since HI and GF are parallel, and given that ∠HAB = 75° and ∠FGH = 286°, use the properties of parallel lines to find the angle ∠J, which is marked as p p p.

STEP 7

Identify the relationship between the angles. Since HI and GF are parallel, the exterior angle ∠FGH and the interior angle ∠J (which is p p p) are supplementary because they form a straight line:∠J+∠FGH=360∘ \text{∠J} + \text{∠FGH} = 360^\circ ∠J+∠FGH=360∘

STEP 8

Substitute ∠FGH = 286° into the equation:p+286∘=360∘ p + 286^\circ = 360^\circ p+286∘=360∘

STEP 9

Solve for p p p:p=360∘−286∘ p = 360^\circ - 286^\circ p=360∘−286∘ p=74∘ p = 74^\circ p=74∘ The value of p p p is:74∘ \boxed{74^\circ} 74∘​

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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.

QuestionDalam Rajah 2, ABCDEFGH ialah sebuah oktagon sekata. Diberi bahawa HI dan GF ialah garis selari.
Cari nilai $p$ .
A $131^{\circ}$
B $136^{\circ}$
C $151^{\circ}$
D $209^{\circ}$

1. ABCDEFGH is a regular octagon.
2. The sum of the interior angles of a polygon with $n$ sides is given by $(n-2) \times 180^\circ$ .
3. HI and GF are parallel lines.
4. We are tasked with finding the value of $p$ .

1. Calculate the interior angle of a regular octagon.
2. Use the properties of parallel lines and angles to find $p$ .

Calculate the sum of the interior angles of the octagon using the formula:
$\text{Sum of interior angles} = (n-2) \times 180^\circ$
where $n = 8$ for an octagon.

Substitute $n = 8$ into the formula:
$\text{Sum of interior angles} = (8-2) \times 180^\circ$ $= 6 \times 180^\circ$ $= 1080^\circ$

Since the octagon is regular, each interior angle is equal. Divide the sum of the interior angles by 8:
$\text{Each interior angle} = \frac{1080^\circ}{8}$ $= 135^\circ$

Since HI and GF are parallel, and given that ∠HAB = 75° and ∠FGH = 286°, use the properties of parallel lines to find the angle ∠J, which is marked as $p$ .

Identify the relationship between the angles. Since HI and GF are parallel, the exterior angle ∠FGH and the interior angle ∠J (which is $p$ ) are supplementary because they form a straight line:
$\text{∠J} + \text{∠FGH} = 360^\circ$

Substitute ∠FGH = 286° into the equation:
$p + 286^\circ = 360^\circ$

Solve for $p$ :
$p = 360^\circ - 286^\circ$ $p = 74^\circ$
The value of $p$ is:
$\boxed{74^\circ}$