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Chapter 12: Q28. (page 696)

A quadrilateral has angle measures of 2x+1,鈭�x-3,鈭�100,鈭� and 3x-2掳. Find the value of x.

Short Answer

Expert verified

The value of x is 44掳.

Step by step solution

01

Step 1. Given Information.

Measurement of the angles of the quadrilateral are 2x+1掳,x-3掳,100掳 and 3x-2掳.

02

Step 2. Concept used.

Sum of all interior angles of a quadrilateral is 360掳.

03

Step 3. Calculation.

According to the problem,

2x+1掳+x鈭�3掳+100掳+3x鈭�2掳=360掳2x+1+x鈭�3+100+3x鈭�2=3602x+x+3x+101鈭�5=3606x=360+5鈭�101

On further simplification,

6x=264x=2646x=44

04

Step 4. Conclusion.

The value of x is 44掳.

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Most popular questions from this chapter

Use the given information to find m鈭�2.

鈭�1 and 鈭�2arevertical angles, and m鈭�1=140掳.

Find m鈭�1.

As shown in the diagram, the two structures of the Puerta de Europa (Door of Europe) in Madrid, Spain, lean toward each other at an angle of 15掳from the vertical.

  1. In the diagram, 鈭�1 and the angle that measures 15掳 are complementary angles. Find m鈭�1.
  2. Tell whether 鈭�1and 鈭�2 arecomplementary or supplementary angles. Then use your answer to part (a) to find m鈭�2.

Tell whether the angles are corresponding, alternate, interior, or alternate exterior angles.

鈭�2and鈭�7

In Exercises 6 and 7, use the given information to find m鈭�2.

鈭�1 and 鈭�2 arecomplementary angles, and m鈭�1=45掳.
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