If the measure of one of the interior angles of a quadrilateral is

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If the measure of one of the interior angles of a quadrilateral is

by BTGmoderatorDC » Fri Jun 17, 2022 5:47 am

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A

B

C

D

E

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If the measure of one of the interior angles of a quadrilateral is 110° what is the sum of the measures of the other 3 interior angles?

A. 220°
B. 250°
C. 300°
D. 330°
E. 360°

OA B

Source: Princeton Review

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Re: If the measure of one of the interior angles of a quadrilateral is

by swerve » Fri Jun 17, 2022 8:54 am
BTGmoderatorDC wrote:
Fri Jun 17, 2022 5:47 am
If the measure of one of the interior angles of a quadrilateral is 110° what is the sum of the measures of the other 3 interior angles?

A. 220°
B. 250°
C. 300°
D. 330°
E. 360°

OA B

Source: Princeton Review
First, recall the following

The sum of all of the interior angles of a quadrilateral is equal to $$360^{\circ}$$

In that way, we have

$$\text{Angle_1}+\text{Angle_2}+\text{Angle_3}+\text{Angle_4}=360^{\circ}$$

We know that one of the interior angles has a measure of $$110^{\circ}$$

Thus,

$$110^{\circ}+\text{Angle_2}+\text{Angle_3}+\text{Angle_4}=360^{\circ}$$
$$\text{Angle_2}+\text{Angle_3}+\text{Angle_4}=360^{\circ}-110^{\circ}$$
$$\text{Angle_2}+\text{Angle_3}+\text{Angle_4}=250^{\circ}$$

Therefore, B

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