# Lesson 11 1 Real World Example 1 Find a Missing Angle Measure 63 x CARPENTRY Mark cuts through the corner of a rectangular board at a 63 angle

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```					Lesson 11-1

Real-World Example 1 Find a Missing Angle Measure
CARPENTRY Mark cuts through the corner of a rectangular
board at a 63 angle.                                       63
a. Classify the relationship between the 63 angle and x. x
The angles at the cut point are complementary.

b. What is the measure of x?
Since the angles are complementary, the sum of their measures is
90°.

mx + 63 = 90           Write the equation.

mx + 63 – 63 = 90 – 63      Subtract 63 from each side.

mx = 27          Simplify.

So, mx = 27.

Example 2 Find Measures of Angles Formed by Parallel Lines
In the figure at the right, m || n and t is a transversal.
a. Classify the relationship between 6 and 1 and the
relationship between 1 and 5.
6 and 1 are alternate exterior angles.
1 and 5 are corresponding angles.

b. If m6 = 55, find m1 and m5.
Since 6 and 1 are alternate exterior angles, they are congruent. So, m1
= m6 = 55.

Since 1 and 5 are corresponding angles, they are congruent. So, m5
= m1 = 55.
Example 3 Use Algebra to Find Missing Angle Measures
ALGEBRA Angles DEF and GHI are supplementary. If mDEF = x – 6 and mGHI =
2x + 9, find the measure of each angle.
Step 1   Find the value of x.
mDEF + mGHI = 180            Supplementary angles

(x – 6) + (2x + 9) = 180     Substitution

3x + 3 = 180      Combine like terms.

3x = 177      Subtract 3 from each side.

x = 59       Divide each side by 3.

Step 2   Replace x with 59 to find the measure of each angle.
mDEF = x – 6                      mGHI = 2x + 9
= 59 – 6 or 53                       = 2(59) + 9 or 127
So, mDEF = 53 and mGHI = 127.

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