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Two angles of a quadrilateral measure 170 and 145 the other two angles are in a ratio of 2:7 what are the measures of those two

User ParagFlume
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1 Answer

3 votes

Answer:

10°, 35°

Explanation:

The sum of angles in a quadrilateral is 360°. This can be used with the angle ratio to find the unknown angles.

Setup

The sum of the two unknown angles, x and y, can be found from the total angle measure in a quadrilateral:

x + y + 170 + 145 = 360

x + y = 45 . . . . . . . . . . . . . subtract 315 from both sides

The ratio of the two angles is ...

x/y = 2/7

7x = 2y . . . . . . cross multiply

Solution

Multiplying the first equation by 2 and substituting for 2y gives ...

2(x +y) = 2(45)

2x +7x = 90

x = 10 . . . . . . . . . divide by 9

y = 45 -10 = 35 . . . . find y

The measures of the other two angles are 10° and 35°.

User Crazybilly
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