The brother-in-law of Brigham Young, he was a member of the vanguard company of Mormon pioneers that entered the Salt Lake Valley on July 24, 1847.

Between the ages of 17 and 19, Angell learned the carpenter and joiner's trade from a man in the neighborhood of his family home.

When the afternoon meeting assembled, Joseph, feeling very much elated, arose the first thing and said the personage who had appeared in the morning was the Angel Peter come to accept the dedication.

He left his wife behind in Winter Quarters and went on with Brigham Young's pioneering company, entering the Salt Lake Valley in July 1847.

Angell's modifications to the Salt Lake Tabernacle in 1870 are said to have resolved the outstanding acoustical issues with that structure.

In 1851, Angell polygamously married Susan Eliza Savage, who had been a textile worker in the Lowell, Massachusetts, cotton mills in the early 1840s until she migrated to Salt Lake City after joining the Church.

Angell was originally asked to also be in charge of the design and construction of the Manti and Logan Temples, but in consequence of their being about 100 miles distant from him in different directions, they were placed in the care of his two assistants.

In April 1856, Young asked Angell to leave his family and go to Europe so that he could learn the architectural designs there.

From 1861 to 1867, Angell had stepped down as Church Architect due to poor health and was replaced by William Folsom.

[3] Even during the time that he was not church architect, Angell worked closely with the construction of the Salt Lake Temple.

Of Angell, Wendell Ashton wrote: "As long as the Salt Lake Temple stands, there will be a magnificent monument to the patience, skill and dedication of its architect.