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Question

Difficulty: EasyLines and Angles

A straight fence is intersected by a diagonal property line. The two adjacent angles formed on the same side of the straight fence are supplementary. If the measure of the smaller angle is represented by x∘x^\circ and the measure of the larger angle is represented by (x+40)∘(x + 40)^\circ, what is the measure of the larger angle?

  1. A
    65∘65^\circ
  2. B
    70∘70^\circ
  3. 110∘110^\circAnswer
  4. D
    150∘150^\circ

Answer

The measure of the larger angle is 110∘110^\circ.
Because the angles are supplementary, their sum must be exactly 180∘180^\circ. By creating the equation x+(x+40)=180x + (x + 40) = 180, we combine the variables to get 2x+40=1802x + 40 = 180. Subtracting 40 from both sides leaves 2x=1402x = 140, making x=70x = 70. Since the larger angle is defined as (x+40)∘(x + 40)^\circ, adding 70 and 40 gives the correct measure of 110∘110^\circ.

Step-by-Step Solution

1
Set up an equation based on the definition of supplementary angles.
x+(x+40)=180x + (x + 40) = 180
Adjacent angles on a straight line are supplementary and must sum to 180 degrees.
2
Combine like terms and isolate the variable xx.
2x+40=180⇒2x=140⇒x=702x + 40 = 180 \Rightarrow 2x = 140 \Rightarrow x = 70
To solve for xx, first subtract 40 from both sides, then divide by 2.
3
Calculate the measure of the larger angle using the expression given in the problem.
(70)+40=110(70) + 40 = 110
The question asks for the larger angle, which is (x+40)∘(x + 40)^\circ, not just the value of xx.

Key Concept

Supplementary Angles and Basic Algebra
Estimated Time:45s
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Topics

Lines and Angles

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