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Below is a rhombus with an equilateral triangle. Find the measure of a.

Below is a rhombus with an equilateral triangle. Find the measure of a.-example-1
User Amindri
by
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1 Answer

21 votes
21 votes

Answer:

a = 80°

Explanation:

In order to solve this figure, we need to find a useful relationship between the various angles. We can use the straight angle at the upper left vertex of the equilateral triangle.

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The sum of angles there is ...

a + 60° +(a/2) = 180°

3/2a = 120° . . . . . . . . . . subtract 60°, collect terms

a = 80° . . . . . . . . multiply by 2/3

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Additional comment

All triangles are isosceles, because they all have 2 (or more) sides the same length. That means the base angles are half the supplement of the a.pex angle. Of course, adjacent vertices of a rhombus have supplementary angles.

Below is a rhombus with an equilateral triangle. Find the measure of a.-example-1
User Dbloch
by
3.6k points