Straight angles Are extremely important in geometry. When two lines intersect , they form multiple angles. In the diagram below,

Question

13 days ago

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Straight angles Are extremely important in geometry. When two lines intersect , they form multiple angles. In the diagram below,

line gm and fh intersect at e. If any of the four angles formed is given, all other three can be found quickly. Fill in the table below.

Mathematics

2 answers:

Inessa [3.9K] · Answer 1 · 2026-02-19T22:43:26+03:00

When two straight lines cross, the vertically opposite angles created are equal, and the remaining two angles match each other as well. Suppose one known angle is x; then the two adjacent angles can be calculated by subtracting twice x from 360 degrees and dividing the remainder by 2.

Thus, the table fills out as follows:

Row 1:

Given angle <GEF = 120°

Angle <FEM is adjacent to <GEF, so
$\angle FEM= \frac{360-2(120)}{2} \\ \\ = \frac{360-240}{2} = \frac{120}{2} =60^o$

Angle <MEH is vertically opposite to <GEF, making it equal to 120°

Angle <HEG is vertically opposite <FEM, so it equals 60°.

Row 2:

Given angle <MEH = 150°

Since <MEH is vertically opposite to <GEF, <GEF = 150°

Angle <FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

Angle <HEG is vertically opposite to <FEM, so <HEG = 30°.

Row 3:

Given angle <FEM = 25°

Angle <FEM is adjacent to <GEF, thus
$\angle GEF= \frac{360-2(25)}{2} \\ \\ = \frac{360-50}{2} = \frac{310}{2} =155^o$

Angle <MEH is vertically opposite to <GEF, equal to 155°

Angle <HEG is vertically opposite <FEM, so it equals 25°.

Row 4:

Given angle <HEG = 45°

Angle <HEG is adjacent to <GEF, so
$\angle GEF= \frac{360-2(45)}{2} \\ \\ = \frac{360-90}{2} = \frac{270}{2} =135^o$

Angle <FEM is vertically opposite to <HEG and thus equals 45°

Angle <MEH is vertically opposite to <GEF, hence <MEH = 135°.

tester [3.9K] · Answer 2 · 2026-02-19T22:45:38+03:00

tester [3.9K]13 days ago

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