UTP angle

Geometry Level 2

$WX$ and $YZ$ are parallel lines and $SV$ and $PR$ are transversals. The size of angle $RQY$ is $61°$ and the size of angle $QUT$ is $42°$

What is the size of angle $UTP$ in degrees?

2 solutions

Munem Shahriar
Jun 6, 2017

Angles RQY and PTX are alternate exterior angles, so are equal

$⇒ ∠PTX = 61°$

Angles QUT and UTX are alternate interior angles, so are equal $⇒ ∠UTX = 42°$

So, $∠UTP = ∠UTX + ∠PTX = 42° + 61° = 103°$

Marta Reece
Jun 6, 2017

$a=61^\circ$

$b=180^\circ -a-42^\circ=180^\circ -61^\circ -42^\circ =77^\circ$

$c=180^\circ -b=180^\circ -77^\circ =\boxed{103^\circ}$