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allochka39001 [22]
2 years ago
5

Find all the unknown angle measures in the diagram. Justify your answer for each angle measure.

Mathematics
1 answer:
Jet001 [13]2 years ago
4 0

Answer:

∠1 is 90° because it is a right angle

To find angle 2, we must add the given angles and x then make the equation equal to 180°, which we next solve for x;

x + 90 + 30 = 180

x + 120 = 180

-120        -120

x = 60, ∠2 = 60°

Angle 5 is vertical to angle 1 which equals 90 degrees, and <u>vertical angles are congruent</u> meaning that they measure the same degrees so therefore ∠5 = 90°

Angles 4 and 40° are <u>vertical</u> to angle 2 which measures 60 degrees;

40 + x(where x equals angle 4) = 60

-40       -40

x = 20, ∠4 = 20°

Specified earlier, angles <u>40° and 4 are equal to 60°</u>, this means that angle three added to angles 40° and 4 will be equal to 90 degrees since angle 1 is 90 degrees and the other three angles will have to equal 90 degrees because they are supplementary.

So we set up the equation;

40 + 20(angle four) + x = 90

60 + x = 90

-60       -60

x = 30, ∠3 = 30°

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