As he got closer, he saw the dark haze billowing out of the doors. Then he heard children screaming.
Angulo, a 36-year-old who is homeless, sprang into action, jumping over a gate and rushing toward the sound of the cries, according to Las Vegas Fire & Rescue.
A 3-year-old girl was standing behind a locked security door on the side of the unit, unable to open it. Angulo pulled at the steel door enough to "bend it upward," officials said. Eventually, the deadbolt unlatched and the door opened.
"The little girl ran to him and wrapped her arms around his waist," Las Vegas Fire & Rescue wrote.
Through the thickening smoke, Angulo could make out an infant's leg on the floor. He dashed back, pulling a 10-month-old baby out of the burning apartment, then moved both children away from the building.
Soon after, firefighters arrived and had the blaze contained after about 10 minutes. Both children were taken to a hospital, where they were treated for smoke inhalation.
Fire officials called Angulo a hero and praised his quick reactions.
"It's obvious if this person hadn't been there, these children could have been burned or may have been killed in the fire," Tim Szymanski, of Las Vegas Fire & Rescue, told KSNV.
"His action certainly saved the children's life," the fire department added in a Facebook post about the incident.
Angulo was reserved when asked about the rescue. "I just knew I had to get them out," he told local media.
Fire officials ruled the blaze an accident. They said a pan of cooking grease ignited on the stove and flames spread rapidly through the small apartment, on the city's east side, several miles from the Strip.
The two children were in the living room when the fire started. Their grandfather was in the back bedroom, fire officials said.
"The kids say the stove caught fire, it got bigger, and they started yelling," Szymanski told KSNV. "The granddad couldn't get to them because of the fire."
The blaze "gutted" the kitchen and living room, and caused an estimated $50,000 in damage, according to the fire department.
"Both kids will be okay," fire officials wrote. "The man is a TRUE HERO."
Las Vegas has one of the highest homelessness rates of any metropolitan area in the country, according to figures from the National Alliance to End Homelessness.
Next year, the city is scheduled to open a "campus" in northern Las Vegas where homeless people will be able to find shelter and access medical care, restrooms, employment assistance and a range of other services, the Las Vegas Review-Journal has reported. The "Corridor of Hope" will be located about two miles from where Angulo pulled the children from the blaze.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)