Use the figure to find the measures of the numbered angles. Explin your reasoning.

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09-11-2017
Mathematics

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Use the figure to find the measures of the numbered angles. Explin your reasoning.

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KaayDuuh KaayDuuh · Answer 1 · 2017-11-20T06:15:58+01:00

1)81° due to the fact that 99° and (1) are supplementary angles
2)99° due to the fact that (5) and (2) are adjacent angles that sum up to equal 180°
3)81° due to the fact that it is the corresponding angle to (5)
4)99° due to the fact that (4) and (2) are alternate interior angles which equal the same
5)81° due to the fact that (5) and (6) are adjacent angles which means they are supplementary angles that add to equal 180°
6)99° due to the fact that (6) and (2) are corresponding angles which equal the same value
7)81° due to the fact that (7) and (3) are corresponding angles with equal the same degree

abidemiokin abidemiokin · Answer 2 · 2021-10-21T13:12:52+02:00

Based on the given diagrams, the measure of the unknown angles are expressed as:

m<1 = 81 degrees

m<2 = 99 degrees

m<3 = 81 degrees

m<4 = 99 degrees

m<5 = 81 degrees

m<6 = 99 degrees

m<7 = 81 degrees

The point where two lines meet is known as an angle.

From the given diagrams, we can see that line "a" is parallel to "b"

Hence we can say that;

m<1 + 99 = 180 (supplementary angles)

m<1 = 180 - 99

m<1 = 81 degrees

m<1 = m<3 = 81 degrees (vertically opposite angles)

m<1 = m<5 = 81 degrees (corresponding angles)

m<5 = m<7 = 81 degrees (vertically opposite angle)

m<4 = 99 degrees (corresponding angle)

m<4 = m<6 = 99 degrees (vertically opposite angles)

Also, m<1 and m<2 are supplementary, hence;

m<1 + m<2 = 180

81 + m<2 = 180

m<2 = 180 - 81

m<2 = 99degrees

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