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.
