Question

use the given information to prove that (mangle rst = mangle vut). given: (mangle1 = mangle4), (mangle2 = mangle3). prove: (mangle rst = mangle vut)

Explanation:

Step1: Express ∠RST in terms of ∠1 and ∠2

$m\angle RST=m\angle1 + m\angle2$

Step2: Express ∠VUT in terms of ∠3 and ∠4

$m\angle VUT=m\angle3 + m\angle4$

Step3: Substitute using given equal - angles

Since $m\angle1 = m\angle4$ and $m\angle2 = m\angle3$, then $m\angle1 + m\angle2=m\angle4 + m\angle3$.

Answer:

$m\angle RST = m\angle VUT$