Question

draw an angle bisector of ∠rst by click and drag to draw a ray from the yellow dot. to redraw, click and drag from the yellow dot again. m∠rst = 58°, m∠rsu = 29°, m∠tsu = 29°. which of the following statements is true? answer: 1. $\frac{1}{2}(mangle{rst})=mangle{rsu}$ 2. m∠rsu = 2(m∠tsu) 3. m∠rst = m∠rsu 4. 2(m∠rsu)=m∠tsu

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal - measure angles. Given $\angle RST = 58^{\circ}$ and $\angle RSU$ and $\angle TSU$ are the two angles formed by the bisector of $\angle RST$, so $\angle RSU=\angle TSU = 29^{\circ}$.

Step2: Check each option

• Option 1: $\frac{1}{2}(m\angle RST)=\frac{1}{2}\times58^{\circ}=29^{\circ}=m\angle RSU$. This is correct.
• Option 2: $m\angle RST = 58^{\circ}$ and $m\angle RSU = 29^{\circ}$, so $m\angle RST

eq m\angle RSU$.

• Option 3: $m\angle RSU = 29^{\circ}$ and $m\angle TSU = 29^{\circ}$, so $m\angle RSU

eq2(m\angle TSU)$.

• Option 4: $2(m\angle RSU)=2\times29^{\circ}=58^{\circ}

eq m\angle TSU$.

Answer:

$\frac{1}{2}(m\angle RST)=m\angle RSU$