Question

which of the following statements is true? answer attempt 1 out of 3 m∠tuv = m∠tuw m∠tuw = m∠vuw 1/2 (m∠tuw) = m∠vuw 2 (m∠tuw) = m∠vuw

Explanation:

Step1: Observe angle - bisector property

From the figure, ray UW is the angle - bisector of ∠TUV. By the definition of an angle - bisector, it divides an angle into two equal angles.
If UW is the angle - bisector of ∠TUV, then m∠TUW=m∠VUW and m∠TUV = m∠TUW + m∠VUW=2m∠TUW = 2m∠VUW.

Step2: Analyze each option

• Option 1: m∠TUV=m∠TUW is false because m∠TUV=m∠TUW + m∠VUW.
• Option 2: m∠TUW=m∠VUW is true as UW is the angle - bisector of ∠TUV.
• Option 3: $\frac{1}{2}(m\angle TUW)=m\angle VUW$ is false. Since m∠TUW = m∠VUW, $\frac{1}{2}(m\angle TUW)

eq m\angle VUW$.

• Option 4: 2(m∠TUW)=m∠VUW is false. Since m∠TUW = m∠VUW, 2(m∠TUW)

eq m∠VUW.

Answer:

m∠TUW = m∠VUW