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Based on the calculations, the value of x and y in this equation are both equal to 5.
<h3>What is a system of linear equations?</h3>A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
<u>Given the following data:</u>
x + y = 10 .....equation 1.
x = 5. .....equation 2.
<h3>How to evaluate an equation.</h3>In order to evaluate the given mathematical equation, we would substitute equation 2 into equation 1 as follows:
y = 5.
Read more on equations here: brainly.com/question/13170908
The Angle HCA is equal to 52°. This is arrived at using the knowledge of the Total value of Angles in a Triangle and the Total Value of Angles in a Polygon.
<h3>What other principles were used to arrive at the answer?</h3>
The other principles of mathematics that were used to arrive at the above answer are:
- Total Angles on a straight line;
- Total Angles on a point; and
- Line segments.
Step 1 - Recall that we have been given Angles AHB and BAH to be 128° and 28° respectively.
We also know that:
- The sum of angles in a triangle is 180°;...................A
- The sum of angles on a straight line is 180°;.........B
- The sum of angles in a polygon is 360°; while.....C
- The total sum of angles at a point is 360°.............D
Since A...therefore:
When ∠AHB (128°) and ∠BAH are taken from 180° we have DBA = ∠28°.
By observation, we can deduce that ∠BDE, ∠CDH, ∠CEH and ∠AEH are all right-angled triangles.
Using the above, we are able to repeat this process of solving for each angle until we have ∠HCA.
To verify that our answer is correct, recall that sum of angles in a polygon is 360°
That means:
∠BDA + ∠DHE + ∠CEH + ∠HCA = 360°
That is, 90+ 128 + 90 + 52 = 360°
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Learn more about Angles in a Triangle at:
brainly.com/question/25215131
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