Question Video: Finding the Measure of an Angle in a Quadrilateral Given the Similar Angle’s Measure in a Similar Quadrilateral | Nagwa Question Video: Finding the Measure of an Angle in a Quadrilateral Given the Similar Angle’s Measure in a Similar Quadrilateral | Nagwa

# Question Video: Finding the Measure of an Angle in a Quadrilateral Given the Similar Angleβs Measure in a Similar Quadrilateral Mathematics • First Year of Secondary School

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Given that π΄π΅πΆπ· is similar to ππππ, find the values of π₯ and π¦.

02:10

### Video Transcript

Given that π΄π΅πΆπ· is similar to ππππ, find the values of π₯ and π¦.

Since these two quadrilaterals are similar, theyβll have the properties of similar polygons. In similar polygons, corresponding angles are congruent and corresponding sides are proportional. Weβll only need the first part of this property: corresponding angles are congruent.

To use this property, we need to identify which angles are corresponding. To do that, we use the names of each quadrilateral. π΄π΅πΆπ· is similar to ππππ. This means the angle at vertex π΄ corresponds to the angle at vertex π. These two angles are congruent, which makes the angle at vertex π 81 degrees. We can also see that the angle at vertex π΅ is congruent to the angle at vertex π. And that means the angle at vertex π΅ must be 97 degrees.

Next, we have the angle at vertex πΆ corresponding to the angle at vertex π. This means we can set up the equation 84 is equal to π¦ plus 35, because we know that the angle at vertex π must be equal to 84 degrees. If we subtract 35 from both sides of this equation, weβll see that π¦ must be equal to 49. Our final pair of corresponding angles is the angle at vertex π· and the angle at vertex π. Therefore, three π₯ plus 65 must equal 98 degrees. If we subtract 65 from both sides of this equation, we find three π₯ equals 33. Dividing both sides by three gives us π₯ equal to 11. Using the property that corresponding angles in similar polygons are congruent, we found that π₯ must be 11 and π¦ equals 49.

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