# ACT Aspire Math: Adding Interior Angles and Linear Triplets

Given that m∠3 = 80°, what is m∠2 + m∠7 + m∠4 + m∠6?

ACT Aspire | Math |

ACT Aspire Math | Geometry |

Math | Geometry |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

All right well let's start out by saying what equations

we can write that use the angles in the given

some and bear with us This isn't simply a neat

thought experiment There's a point to it way Swear well

the sum of any triangle's interior angles one hundred eighty

degrees So seven plus three plus six there is one

hundred eighty degrees right That's at least a foundational base

we can work with Used this equation Isolate angle six

and seven and apply the fact that the angle three

is eighty degrees So if we do that we get

well Angle seven and six are one eighty Then we

take one eighty and subtract that angle Three there and

that gets us a hundred degrees So angle's too three

and four form a linear triplet so angle two three

and four are one hundred eighty degrees Well we can

isolate angles two and four and use the measure of

angle three once again right So we have angle too

And for our one hundred eighty degrees Then subtract ingle

three's eighty and that gets us a hundred degrees Well

knowing that angle to plus angle Seven plus angle Four

plus angle Six is basically just one hundred plus one

hundred or two hundred degrees in angularity So the answer 00:01:31.521 --> [endTime] they arrest you See that's it Two hundred baby