It is known from the condition that the sum of two angles is 300 °, and the difference between these angles is 80 °. In order to find these angles, we will compose and solve a system of equations.
Let us denote by the variable x the degree measure of the first angle, and by the variable y the degree measure of the second angle.
We make up the system:
x + y = 300;
x – y = 80.
We solve the system by the addition method.
x + x = 300 + 80;
y = 300 – x.
We solve the first equation of the system:
2x = 380;
x = 380: 2;
x = 190 ° degree measure of the first angle,
y = 300 – 190 = 110 ° the degree measure of the second angle.
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