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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 18 Page 75

Angles marked with the same angle marker are congruent.

x=7

Practice makes perfect

We have been asked to find the value of x using the given expressions for m∠ BDK and m∠ JDR. The expression m∠ BDK is the angle measure between the rays DB and DK. Similarly, m∠ JDR is the angle measure between the rays DJ and DR.

Looking at the figure, we should notice that angles ∠ BDK and ∠ JDR have been marked with the same angle marker, which means they are congruent. Therefore, their measures have to be the same. Let's write this fact as an equation. m∠ BDK = m∠ JDR Let's substitute the expressions 3x+4 and 5x-10 for m∠BDK and m∠JDR, respectively, in the above equation. Then we can solve for x.

m∠ BDK = m∠ JDR

SubstituteExpressions

Substitute expressions

3x+4 = 5x-10

▼

Solve for x

LHS+10=RHS+10

3x+14=5x

LHS-3x=RHS-3x

14 = 2x

.LHS /2.=.RHS /2.

7 = x

Rearrange equation

x=7

We have found that x=7.