Question 554850
Let the angles be a,b, and c
given:
(1) {{{ a + b + c = 180 }}}
(2) {{{ a = 4b }}}
(3) {{{ c = b + 78 }}}
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This is 3 equations and 3 unknowns,
so it's solvable
Substitute (2) and (3) into (1)
(1) {{{ 4b + b + b + 78 = 180 }}}
(1) {{{ 6b = 180 - 78 }}}
(1) {{{ 6b = 102 }}}
(1) {{{ b = 17 }}}
and, since
(2) {{{ a = 4b }}}
(2) {{{ a = 4*17 }}}
(2) {{{ a = 68 }}}
and
(3) {{{ c = b + 78 }}}
(3) {{{ c = 17 + 78 }}}
(3) {{{ c = 95 }}}
The angles are 68, 17, and 95 degrees
check:
{{{ 68 + 17 + 95 = 180 }}}
{{{ 180 = 180 }}}
OK