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Three angles of a quadrilateral are 75∘, 90∘ and 75∘. The measure of fourth angle is? A. 90∘ B. 95∘ C. 105∘ D. 120∘

1 Answer

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Answer:

120⁰

Explanation:

The angles of a quadrilateral always add up to 360⁰.

Think of a square: it has four 90⁰ angles, right? That's 360⁰.

So since you're given 3 of the angles, you just need to add them up and see how much more you need to get to 360⁰:

75 + 90 + 75 = 240⁰

You should be able to see from there that you need 120⁰ more to get to 360⁰. So that's the unknown angle.

But to do it with algebra looks like this:

75 + 90 + 75 + x = 360

Where x = the unknown angle. Solve for x:

x = 360 - (75 + 90 + 75) = 120⁰

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