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<5 and <6 are vertical angles. if m<5 = 6x and m<4 = 4x + 6 find the measures of the two angles

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Sagot :

AuLlorenidn

Answer:

<5 = 104.4

<4 = 75.6

Step-by-step explanation:

If <5 and <6 are vertical angles, then <5 and <4 are complementary angles

Complementary angles are angles that has a sum of 180 degrees altogether

<5= 6x

<4= 4x+6

So, <5 + <4 = 180°

---(6x) + (4x+6) = 180°

---10x + 6= 180°

---10x = 180 - 6

---10x = 174

---10x/10 = 174/10

---x = 17.4

Substitute:

<5= 6x

---6 (17.4)= 104.4

<4= 4x+6

---4 (17.4) + 6 = 75.6

Answer with Step-by-step explanation:

Vertical angles are congruent.

∠5 = ∠6

Linear angles are supplementary.

∠5 and ∠4  are supplementary.  The sum of their measures is 180°

Given:

  • m∠5 = 6x
  • m∠4 = 4x + 6

Equation:

(6x) + (4x+6) = 180

Find x:

10x + 6 = 180

10x = 180 - 6

10x/10 = 174/10

x = 17.4

Answer:

The measures of the angles:

m∠ 4 = 4(17.4) + 6

m ∠ 4 =69.6 + 6

m∠4 = 75.6°

m∠5 = 6(17.4)

m∠5 = 104.4°

m∠6 = 104.4°