Question

use the given information to prove that ( mangle qps = mangle tpv ).

given: ( mangle 1 = mangle 2 )
( mangle 3 = mangle 4 )
prove: ( mangle qps = mangle tpv )

Explanation:

Step1: Express \(m\angle QPS\)

By angle addition postulate, \(m\angle QPS=m\angle1 + m\angle3\)

Step2: Express \(m\angle TPV\)

By angle addition postulate, \(m\angle TPV=m\angle2 + m\angle4\)

Step3: Substitute using given equalities

Since \(m\angle1 = m\angle2\) (given) and \(m\angle3 = m\angle4\) (given), substitute into the expressions:
\(m\angle QPS=m\angle2 + m\angle4\)

Answer:

Since \(m\angle QPS=m\angle2 + m\angle4\) and \(m\angle TPV=m\angle2 + m\angle4\), we have \(m\angle QPS = m\angle TPV\)