Question

given: ∠1 is an exterior angle of △urs. prove: m∠r = m∠1 - m∠3

Explanation:

Step1: State the given

$\angle1$ is an exterior angle of $\triangle URS$

Step2: Apply exterior - angle theorem

By the Exterior Angle of a Triangle Theorem, $m\angle1=m\angle R + m\angle3$

Step3: Subtract $m\angle3$ from both sides

Using the Subtraction Property, $m\angle1 - m\angle3=m\angle R + m\angle3 - m\angle3$

Step4: Simplify the right - hand side

After simplifying $m\angle R + m\angle3 - m\angle3$, we get $m\angle R=m\angle1 - m\angle3$

Answer:

1. $\angle1$ is an exterior angle of $\triangle URS$
2. $m\angle1=m\angle R + m\angle3$
3. $m\angle1 - m\angle3=m\angle R + m\angle3 - m\angle3$
4. $m\angle R=m\angle1 - m\angle3$