We know that
The inscribed angle Theorem states that t<span>he inscribed angle measures half of the arc it comprises.
</span>so
m∠D=(1/2)*[arc EFG]
and
m∠F=(1/2)*[arc GDE]
arc EFG+arc GDE=360°-------> full circle
applying multiplication property of equality
(1/2)*arc EFG+(1/2)*arc GDE=180°
applying substitution property of equality
m∠D=(1/2)*[arc EFG]
m∠F=(1/2)*[arc GDE]
(1/2)*arc EFG+(1/2)*arc GDE=180°----> m∠D+m∠F=180°
the answer in the attached figure
<u>Define x and y:</u>
Let the first number be x and the second number be y.
<u>Setup the equations:</u>
y + 2x = 10 ----------- (1)
2y + x = 11 ----------- (2)
<u>Solve x;</u>
From (1):
y + 2x = 10
y = 10 - 2x ----------- Sub into (2)
2(10 - 2x) + x = 11
20 - 4x + x = 11
20 - 3x = 11
3x = 20 - 11
3x = 9
x = 3 ----------- Sub into (1)
y + 2(3) = 10
y = 10 - 6
y = 4
<u>Find the numbers:</u>
First number = x = 3
Second number = y = 4
Answer: The two numbers are 3 and 4.