Answer:
A is 65 and B is 25
Step-by-step explanation:
1st Equation: A = 2B + 15
2nd Equation: A + B = 90
A + B = 90
A = 90 - B
Substitute: 90 - B = 2B + 15
3B = 75
B = 25
A + 25 = 90
A = 65
A = 65
B = 25
Answer:
m∠A = 65°
m∠B = 25°
Step 1: Remembering the notions
To solve this problem, we we must know that depending on the sum of the measures of two angles, the angles can be:
So, m∠A (a)+ m∠B (b) = 90
We write the equation:
[tex]a+b=90[/tex]
[tex]a=2b+15[/tex]
Step 2: Solve the System
[tex]\left \bigerwille \{ {{a+b=90} \atop { a=2b+15}} \right.[/tex] ⇔[tex]\left \bigerwille \{ {{2b+15+b=90} \atop{a=2b+15}} \right.[/tex]
We can write this matematically as,
[tex]\rightarrow2b +15 +b = 90[/tex]
Move the constant to the right,
[tex]\rightarrow 3b=90-15[/tex]
Divide both sides
[tex]\rightarrow3b=75[/tex] ⇒ [tex]b = \frac{75}{3}=25[/tex]
[tex]\left \{ {{a+b = 90} \atop {b = 25}} \right.[/tex]⇔ [tex]\left \{ {{a=75} \atop {b=2}5} \right.[/tex]
Step 3: Answer the Question
We now know what m∠A = 65° and m∠B = 25°.
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