The measures of two interior angles of a triangle are 67° and 102°. What is the measure of the third angle?
2 answers:
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Based on the given parameters of the question the correct angles are as follows;
The measure of the large angle is <u>155°</u>, and the measure of the small angle is <u>25°</u>
The reasons the above values are correct are given as follows:
The given parameters are;
The properties of the two angles = Supplementary angles (sum of 180°)
The measure of the larger angle = 7 × The measure of smaller angle - 20°
Required:
To find the measure of each angle algebraically
Solution:
An algebraic equation can be described as a mathematical expression having an equal to sign that relates variables representing unknown values or quantities
Let <em>L</em>, represent the measure of the larger angle and let <em>S</em>, represent the measure of the smaller angle, we have;
L + S = 180°...(1)
L = 7 × S - 20°...(2)
Therefore;
Plugging in the value of <em>L</em> from equation (2) in equation (1) gives;
L + S = 7 × S - 20 + S = 180
7·S + S - 20 = 180
Adding 20 to both sides gives;
7·S + S - 20 + 20 = 180 + 20 (addition property of equality)
8·S =180 + 20 = 200
The measure of the small angle, S = <u>25°</u>
L = 7 × S - 20
∴ L = 7 × 25 - 20 = 155
The measure of the large angle, L = <u>155°</u>
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