Question

A quadrilateral has three angles that measure 80°, 110°, and 75°. Which is the measure of the fourth angle? A. 50° B. 90° C. 95° D. 125°

Answer 1

a quadrilateral has 4 angles that add up to 360 degrees

x + 80+110+ 75 = 360

combine like  terms

x + 265 = 360

subtract 265 from each side

x + 265 -265 =360 -265

x = 95

Choice C

Answer 2

Answer:

C. 95°

Step-by-step explanation:

Since the sum of the interior angles of any triangle is 180 ° and there are two triangles in a quadrilateral, the sum of the angles of all the quadrilaterals is 360 °.

Let us denote the angles with the letter "A", so that their values are:

A1 = 80°

A2 = 110°

A3 = 75°

A4 =?

So, applying the rule without exceptions that a quadrilateral has 4 angles that add up to 360°, we have

A1 + A2 + A3 + A4 = 360°

Isolating A4 and substituting the values, we obtain the value of the fourth angle:

A4 = 360° - A1 - A2 - A3

A4 = 360° - 80° - 110° - 75°

A4 = 95°  

The correct option is C. 95°

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