Chapter 12: Q28. (page 696)

A quadrilateral has angle measures of $(2 x + 1) {}^{\circ}, (x - 3) {}^{\circ}, 100 {}^{\circ},$ and $(3 x - 2) °$ . Find the value of x.

Short Answer

Expert verified

The value of x is $44 °$ .

Step by step solution

Step 1. Given Information.

Measurement of the angles of the quadrilateral are $(2 x + 1) °$ , $(x - 3) °$ , $100 °$ and $(3 x - 2) °$ .

Step 2. Concept used.

Sum of all interior angles of a quadrilateral is $360 °$ .

Step 3. Calculation.

According to the problem,

$\begin{matrix} (2 x + 1) ° + (x - 3) ° + 100 ° + (3 x - 2) ° = 360 ° \\ 2 x + 1 + x - 3 + 100 + 3 x - 2 = 360 \\ 2 x + x + 3 x + 101 - 5 = 360 \\ 6 x = 360 + 5 - 101 \end{matrix}$

On further simplification,

$\begin{matrix} 6 x = 264 \\ x = \frac{264}{6} \\ x = 44 \end{matrix}$

Step 4. Conclusion.

The value of x is $44 °$ .

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A quadrilateral has angle measures of $(2 x + 1) {}^{\circ}, (x - 3) {}^{\circ}, 100 {}^{\circ},$ and $(3 x - 2) °$ . Find the value of x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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A quadrilateral has angle measures of 2x+1,∘x-3,∘100,∘ and 3x-2°. Find the value of x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Probability and Statistics

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A quadrilateral has angle measures of $(2 x + 1) {}^{\circ}, (x - 3) {}^{\circ}, 100 {}^{\circ},$ and $(3 x - 2) °$ . Find the value of x.