Question

tv is parallel to wx. the distance between tv and wx is always 6 units. vw is 10 units long. m∠1 = 36.87°. li was asked to find the measure of ∠2 and explain his reasoning. fill in the blanks in lis solution. we were given the distance between the parallel lines, so both uw and yv have a length of units. △vuw and △wyv share a side, and we were given that this side is 10 units long. both △vuw and △wyv are right - triangles, so we can use the pythagorean theorem to find the lengths of vu and wy. vu and wy both have a length of units. △vuw ≅ △wyv by the side - side - side congruency postulate. m∠2= ° since ∠1 and ∠2 are corresponding parts of congruent triangles.

Explanation:

Step1: Recall distance between parallel lines

The distance between parallel lines $\overleftrightarrow{TV}$ and $\overleftrightarrow{WX}$ is given as 6 units. So, the length of $\overline{UW}$ and $\overline{YV}$ is 6 units.

Step2: Apply Pythagorean theorem

In right - triangle $\triangle VUW$, $VW = 10$ units and $UW=6$ units. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = VW$, $a = UW$, and $b = VU$. So, $VU=\sqrt{VW^{2}-UW^{2}}=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$ units. Similarly, for right - triangle $\triangle WYV$, $WY = 8$ units.

Step3: Use congruence of triangles

Since $\triangle VUW\cong\triangle WYV$ by SSS (Side - Side - Side) congruency postulate and $\angle1$ and $\angle2$ are corresponding parts of congruent triangles, $m\angle2=m\angle1$.

Answer:

• First blank: 6
• Second blank: 8
• Third blank: 36.87