m ∠1 + m ∠2= since they are supplementary angles. Since m ∠1 = m ∠2, then m ∠1 + m ∠1=180^(∘) by . Solving the equation gives m ∠1 = . Since m ∠1 = m ∠2, then m∠2 is also . Therefore, ∠1 and ∠2 are right angles.
Let's do it! First, if two angles are supplementary, then by definition their angle measures add up to 180^(∘). We can fill in the first gap.
Given
m ∠1 = m ∠2, ∠1 and ∠2 are supplementary.
Prove
∠1 and ∠2 are right angles.
Proof
m ∠1 + m ∠2= 180^(∘) since they are supplementary angles. Since m ∠1 = m ∠2, then m ∠1 + m ∠1=180^(∘) by . Solving the equation gives m ∠1 = . Since m ∠1 = m ∠2, then m∠2 is also . Therefore, ∠1 and ∠2 are right angles.
Now, we can rewrite the second sentence of the proof using mathematical symbols.
m ∠1 = m ∠2 ⇒ m ∠1 + m ∠1=180^(∘)
We see that m ∠1 was substituted for m ∠2 in the expression. The resulting statement is still true because the angle measures are equal.
Given
m ∠1 = m ∠2, ∠1 and ∠2 are supplementary.
Prove
∠1 and ∠2 are right angles.
Proof
m ∠1 + m ∠2= 180^(∘) since they are supplementary angles. Since m ∠1 = m ∠2, then m ∠1 + m ∠1=180^(∘) by substitution. Solving the equation gives m ∠1 = . Since m ∠1 = m ∠2, then m∠2 is also . Therefore, ∠1 and ∠2 are right angles.
To solve the resulting equation, we should isolate m ∠1 on one side of the equation. Let's do it!
We found that m ∠1=90^(∘). Let's write that down.
Given
m ∠1 = m ∠2, ∠1 and ∠2 are supplementary.
Prove
∠1 and ∠2 are right angles.
Proof
m ∠1 + m ∠2= 180^(∘) since they are supplementary angles. Since m ∠1 = m ∠2, then m ∠1 + m ∠1=180^(∘) by substitution. Solving the equation gives m ∠1 = 90^(∘). Since m ∠1 = m ∠2, then m∠2 is also . Therefore, ∠1 and ∠2 are right angles.
Because angles 1 and 2 have the same measure, we know that m∠2 is also 90^(∘).
Given
m ∠1 = m ∠2, ∠1 and ∠2 are supplementary.
Prove
∠1 and ∠2 are right angles.
Proof
m ∠1 + m ∠2= 180^(∘) since they are supplementary angles. Since m ∠1 = m ∠2, then m ∠1 + m ∠1=180^(∘) by substitution. Solving the equation gives m ∠1 = 90^(∘). Since m ∠1 = m ∠2, then m∠2 is also 90^(∘). Therefore, ∠1 and ∠2 are right angles.
