GCSE OCR Maths Angle Facts: An interior angle of an isoscele

An interior angle of an isosceles triangle is $p^o$ and an exterior angle is $q^o$ - OCR - GCSE Maths - Question 10 - 2019 - Paper 5

Question 10

An interior angle of an isosceles triangle is $p^o$ and an exterior angle is $q^o$. It is given that $q = 5p$. (a) Write the ratio $p : q$ in its simplest form. ... show full transcript

Worked Solution & Example Answer:An interior angle of an isosceles triangle is $p^o$ and an exterior angle is $q^o$ - OCR - GCSE Maths - Question 10 - 2019 - Paper 5

Step 1

(a) Write the ratio $p : q$ in its simplest form.

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Answer

To find the ratio $p : q$ , we start from the given relationship between $q$ and $p$ :

$q = 5p$

Now we can express the ratio as:

$p : q = p : 5p$

When we simplify this ratio, we divide both terms by $p$ (assuming $p eq 0$ ):

$p : 5p = 1 : 5$

Thus, the ratio $p : q$ in its simplest form is:

$1 : 5$

Step 2

(b) Work out the two different possible sets of angles for the isosceles triangle.

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Answer

In an isosceles triangle, two angles are equal. Let’s denote the interior angles:

The interior angle is $p$
The exterior angle is $q = 5p$

The relationship between the interior and exterior angle is given by:

$q + p = 180$

Substituting for $q$ , we get:

$5p + p = 180$

This simplifies to:

$6p = 180$

Solving for $p$ , we find:

$p = 30$

Using this value, we calculate $q$ :

$q = 5p = 5 imes 30 = 150$

The angles of the isosceles triangle can be:

$30$ , $30$ , and $120$ (when the two equal angles are the interior angles)
$30$ , $150$ , and $30$ (when the $150$ degree angle is the exterior angle opposite to the equal sides)

Thus, the two possible sets of angles for the isosceles triangle are:

$30^o, 30^o, 120^o$
$30^o, 150^o, 30^o$

An interior angle of an isosceles triangle is $p^o$ and an exterior angle is $q^o$ - OCR - GCSE Maths - Question 10 - 2019 - Paper 5

Worked Solution & Example Answer:An interior angle of an isosceles triangle is $p^o$ and an exterior angle is $q^o$ - OCR - GCSE Maths - Question 10 - 2019 - Paper 5

(a) Write the ratio $p : q$ in its simplest form.

(b) Work out the two different possible sets of angles for the isosceles triangle.

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