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Chapter 12: Q35. (page 691)

Let ∠1and ∠2be complementary angles, and let ∠2and ∠3be supplementary angles. If m∠1=x° and m∠2=2x°, find x. Then find m∠1, m∠2, and m∠3.

Short Answer

Expert verified

The value of x is30°. m∠1=30,∘m∠2=60,∘and m∠3=120°

Step by step solution

01

Step 1. Given Information.

m∠2=2xand∘m∠1=x°

02

Step 2. Calculation.

Since, complementary angles are those whose sum of the angles is 90°. That is,

m∠1+m∠2=90°

…… (1)

Find x using equation (1).

x°+2x°=90°3x°=90°x=90°3°x=30°

Thus, the value of x is 30°.

Therefore, the angle measures are 30°, 60°.

Also, supplementaryangles are those whose sum of the angles is 180°. That is,

m∠2+m∠3=180° ……. (2)

Find x using equation (2).

m∠2+m∠3=180°

Since, m∠2=60°

Therefore, the equation (2) becomes,

60°+m∠3=180°m∠3=180°−60°m∠3=120°

Therefore, m∠3=120°.

03

Step 3. Conclusion.

The angles are m∠1=30,∘m∠2=60,∘ and m∠3=120°.

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Most popular questions from this chapter

In Exercises 32 and 33, use the diagram.

Which numbered angles have the same measure as ∠1? Explain your reasoning.

In Exercise 3-6, match the description with correct value.

Measures of interior angles of a regular hexagon.

The drawing is a herring illusion, in which intersecting transversal make two parallel lines appear to be curves. Describe a way you can use a protector to verify that the two lines are parallel.

Use the diagram. For lines mand nto be parallel, what must the value of xbe?

  1. Tell whether the labelled angles are corresponding, alternate interior, or alternate exterior angles.
  2. Write an equation that relates the angles measures.
  3. Solve the equation for x.

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

∠1 and ∠2 aresupplementary angles, and m∠1=160°.
See all solutions

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