Question

Two angles are supplementary. The measure of the larger angle is 20 degrees

Answer 1

Based on the given parameters of the question the correct angles are as follows;

The measure of the large angle is 155°, and the measure of the small angle is 25°

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 L, represent the measure of the larger angle and let S, represent the measure of the smaller angle, we have;

L + S = 180°...(1)

L = 7 × S - 20°...(2)

Therefore;

Plugging in the value of L 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

$S = \dfrac{200}{8} = 25$

The measure of the small angle, S = 25°

L = 7 × S - 20

∴ L = 7 × 25 - 20 = 155

The measure of the large angle, L = 155°

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