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°

Question

kotykmax [81]

2 years ago

10

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°

Mathematics

2 answers:

Free_Kalibri [48] · Answer 1 · 2022-04-28T22:59:15+03:00

Free_Kalibri [48]2 years ago

5 0

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

Step2247 [10] · Answer 2 · 2022-04-29T01:21:06+03:00

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°

Hpe this hepls!