Question
Two adjacent angles, ∠1
∠
1
and ∠2
∠
2
, form a resulting angle with measure 135°. If m∠1=(2x)° and m∠2=(2x+7)°, what are the two unknown angle measures?
∠
1
and ∠2
∠
2
, form a resulting angle with measure 135°. If m∠1=(2x)° and m∠2=(2x+7)°, what are the two unknown angle measures?
Answers
GPT 3.5
To solve this problem, we can set up an equation by adding the measures of ∠1 and ∠2 and setting it equal to 135°:
m∠1 + m∠2 = 135°
Substitute (2x)° for m∠1 and (2x+7)° for m∠2:
2x + 2x + 7 = 135
Combine like terms:
4x + 7 = 135
Subtract 7 from both sides to isolate the term with x:
4x = 128
Divide both sides by 4 to solve for x:
x = 32
Now we can substitute this value back into the expressions for m∠1 and m∠2 to find their measures:
m∠1 = (2x)° = 2(32)° = 64°
m∠2 = (2x + 7)° = 2(32) + 7° = 71°
Therefore, the unknown angle measures are m∠1 = 64° and m∠2 = 71°.
m∠1 + m∠2 = 135°
Substitute (2x)° for m∠1 and (2x+7)° for m∠2:
2x + 2x + 7 = 135
Combine like terms:
4x + 7 = 135
Subtract 7 from both sides to isolate the term with x:
4x = 128
Divide both sides by 4 to solve for x:
x = 32
Now we can substitute this value back into the expressions for m∠1 and m∠2 to find their measures:
m∠1 = (2x)° = 2(32)° = 64°
m∠2 = (2x + 7)° = 2(32) + 7° = 71°
Therefore, the unknown angle measures are m∠1 = 64° and m∠2 = 71°.