The Southern California native was 27.
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Skaggs was found unconscious in a hotel room in Southlake, Texas, according to police in that city. The team was scheduled to play the Rangers later Monday.
Officers found him unresponsive at 2:18 p.m. in a room at the Hilton. He was pronounced dead at the scene.
"At this time, no foul play is suspected," the Southlake Police Department said. "This investigation is ongoing and we will release pertinent information as it is available."
"We would like to extend our condolences to the Skaggs family and to the Los Angeles Angels organization."
"It is with great sorrow that we report Tyler Skaggs passed away earlier today in Texas," the team wrote on Twitter. "Tyler has, and always will be, an important part of the Angels Family. Our thoughts and prayers are with his wife Carli and his entire family during this devastating time."
The Angels game scheduled for Monday against the Rangers in Texas has been canceled, the team said.
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Skaggs was born in the Woodland Hills neighborhood of Los Angeles and went to high school in Santa Monica. Though his high school was just across town from Dodger Stadium, he grew up rooting for the Angels.
His mother, Debbie, was the longtime softball coach at Santa Monica High School and is still a physical education teacher there. She famously provided postgame tips on his pitching mechanics, even deep into his big-league career.
Even as a major-leaguer, he continued to visit his old school to help students there, according to Santa Monica-Malibu Unified School District Superintendent Ben Drati.
"Tyler continued to make visits to our schools the past several years to speak with students and we proudly watched his ascent in professional baseball, along with his family," Drati said. "Tyler's mother, Debbie, was a previous girls softball coach at Samohi and is currently a physical education teacher."
"Our thoughts and prayers are with his family, friends and fans during this difficult time."
Skaggs was drafted by the Angels in 2009 out of high school but was then traded to the Arizona Diamondbacks before making his Major League Baseball debut. He returned to the Angels in a trade in 2013.
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Skaggs, who would have turned 28 on July 13, had been a regular in the Angels' starting rotation since late 2016, when he returned from Tommy John surgery. He struggled with injuries repeatedly over the past three seasons but persevered to become a valuable starter in Los Angeles' injury-plagued rotation.
The left-hander had just pitched on Saturday, allowing two runs in 4 1/3 innings in a 4-0 loss to Oakland.
Baseball Commissioner Rob Manfred said he was "deeply saddened" by Skaggs' death.
"We will support the Angels' organization through this most difficult period, and we will make a variety of resources available to Tyler's teammates and other members of the baseball family," Manfred said in a statement.
Skaggs started a career-high 24 games last season, going 8-10 with a 4.02 ERA. He missed playing time in April this season with a sprained ankle but came back strong.
The Associated Press contributed to this report.