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The diagram shows how a rhombus is made by joining two equilateral triangles - OCR - GCSE Maths - Question 6 - 2021 - Paper 3
Question 6
The diagram shows how a rhombus is made by joining two equilateral triangles. (a) Find the size of each interior angle of the rhombus. (b) The same rhombus can be ... show full transcript
Worked Solution & Example Answer:The diagram shows how a rhombus is made by joining two equilateral triangles - OCR - GCSE Maths - Question 6 - 2021 - Paper 3
Step 1
Find the size of each interior angle of the rhombus.
Answer
To find the size of each interior angle of the rhombus, we can utilize the properties of equilateral triangles. Each equilateral triangle has angles of 60 degrees. Since two of these triangles make up the rhombus, we note that two angles of the rhombus are formed by the apexes of the triangles.
In the rhombus, the angles opposite each other are equal. Therefore, the size of each interior angle of the rhombus can be calculated as:
Thus, each interior angle of the rhombus is 120 degrees.
Step 2
Find the size of each angle of the isosceles triangle.
Answer
For the isosceles triangle making up the rhombus, we need to ensure that the angles also sum up to 180 degrees. Let's denote the equal angles as 'x' and the angle opposite the base as 'y'. Since the two triangles are congruent in terms of forming the rhombus, each will share the same angle.
Thus, we have the equation:
We also know that the angle 'y' formed from the rhombus is 120 degrees since we derived it earlier. Therefore, substituting for 'y':
Solving for 'x', we get:
Thus, each angle of the isosceles triangle is 30 degrees for the equal angles, and the base angle is 120 degrees.