Find the measures of missing angles of triangles Find the measures of missing remote interior and exterior angles

1. Triangle Angle Relationships
The student is able to (I can):
• Find the measures of missing angles of triangles
• Find the measures of missing remote interior and exterior
angles

2. Triangle Angle Sum TheoremTriangle Angle Sum TheoremTriangle Angle Sum TheoremTriangle Angle Sum Theorem – all angles of a triangle add up
to 180°.
Example: Find the measure of the missing angle
56˚ 29˚
180 – (56 + 29) = 180 – 85 = 95˚

3. corollarycorollarycorollarycorollary – a theorem whose proof follows directly from
another theorem.
Right TriangleRight TriangleRight TriangleRight Triangle CorollaryCorollaryCorollaryCorollary – the acute angles of a right triangle
are complementary.
A
B C
m∠A+m∠B+m∠C=180˚
m∠A + 90˚ + m∠C = 180˚
m∠A + m∠C = 90˚

4. Equiangular TriangleEquiangular TriangleEquiangular TriangleEquiangular Triangle CorollaryCorollaryCorollaryCorollary – the measure of each angle of
an equiangular triangle is 60˚.
E
Q
U
m∠E = m∠Q = m∠U
m∠E + m∠Q + m∠U = 180˚
m∠E + m∠E + m∠E = 180˚
3(m∠E) = 180˚
m∠E = 60˚

5. interiorinteriorinteriorinterior angleangleangleangle – the angle formed by two sides of a polygon
exteriorexteriorexteriorexterior angleangleangleangle – the angle formed by one side of a polygon
and the extension of an adjacent side
remote interiorremote interiorremote interiorremote interior angleangleangleangle – an interior angle that is not adjacent
to an exterior angle
1
2222
3333 4444
interiorinteriorinteriorinterior
exterior

6. Exterior AngleExterior AngleExterior AngleExterior Angle TheoremTheoremTheoremTheorem – the measure of an exterior angle of
a triangle is equal to the sum of its remote interior
angles.
m∠3 + m∠4 = m∠1 + m∠2 + m∠3
m∠4 = m∠1 + m∠2
1
2222
3333 4444
interiorinteriorinteriorinterior
exterior

7. Practice
1. What is m∠1?
2. Solve for x
140°
105°
1
15°
(2x+3)°
(5x‒60)°

8. Practice
1. What is m∠1?
2. Solve for x
140°
105°
1
15°
(2x+3)°
(5x‒60)°
140 = 105 + m∠1
m∠1 = 35°
5x – 60 = 2x + 3 + 15
5x – 60 = 2x + 18
3x – 60 = 18
3x = 78
x = 26