GEOMETRYHELP

m ACB = 90 Definition of right angle

Find c first, using the fact that ACB is a right angle.

c + 70 = 90 Angle Addition Postulate

c = 20 Subtract 70 from each side.

Parallel Lines and the Triangle Angle-Sum TheoremLESSON 3-4

Additional Examples

In triangle ABC, ACB is a right angle, and CD AB.

Find the values of a, b, and c.

GEOMETRYHELP

a + m ADC + c = 180 Triangle Angle-Sum Theorem

m ADC = 90 Definition of perpendicular lines

a + 90 + 20 = 180 Substitute 90 for m ADC and 20 for c.

a + 110 = 180 Simplify.

a = 70 Subtract 110 from each side.

70 + m CDB + b = 180 Triangle Angle-Sum Theorem

m CDB = 90 Definition of perpendicular lines

70 + 90 + b = 180 Substitute 90 for m CDB.

160 + b = 180 Simplify.

b = 20 Subtract 160 from each side.

To find b, use CDB.

To find a, use ADC.

(continued)

Quick Check

Parallel Lines and the Triangle Angle-Sum TheoremLESSON 3-4

Additional Examples

GEOMETRYHELP

The three sides of the triangle have three different lengths, so the triangle is scalene.

One angle has a measure greater than 90, so the triangle is obtuse.

The triangle is an obtuse scalene triangle.

Classify the triangle by its sides and its angles.

Quick Check

Parallel Lines and the Triangle Angle-Sum TheoremLESSON 3-4

Additional Examples

GEOMETRYHELP

Find m1.

m1 + 90 = 125 Exterior Angle Theorem

m1 = 35 Subtract 90 from each side.

Parallel Lines and the Triangle Angle-Sum TheoremLESSON 3-4

Additional Examples

Quick Check

GEOMETRYHELP

Explain what happens to the angle formed by the back of the

chair and the armrest as you make a lounge chair recline more.

The exterior angle and the angle formed by the back of the chair and the armrest are adjacent angles, which together form a straight angle. As one measure increases, the other measure decreases.

The angle formed by the back of the chair and the armrest increases as you lower the back of the lounge chair.

Parallel Lines and the Triangle Angle-Sum TheoremLESSON 3-4

Additional Examples

Quick Check