given that ABC and BED are straight lines,find the values of the unkno

1.	given that ABC and BED are straight lines,find the values of the unknowns in each of the following figures
Answer» Step-by-step EXPLANATION: GIVEN: Given that ABC and BED are straight lines,FIND the values of the unknowns. To find:a° and b° Solution: ABC is straight line. $\angle \: ABE + \angle \: EBC = 180° \\ \\ \angle \: EBC = 180° - 115° \\ \\ \angle \: EBC = 65° \\ \\$ To find: a° In ∆BCE, since angle BCE= 90° apply angle SUM property of triangle $\angle \: EBC + \angle \: BCE + \angle \: a = 180° \\ \\ 65° + 90° + \angle \: a = 180° \\ \\ \angle \: a = 180° - 155° \\ \\ \angle \: a = 25° \\ \\$ To find b°: Since BED is a straight line $\angle \: a + \angle \: FEG + \angle \: b = 180° \: \: \: ...eq1 \\ \\ (angles \: on \: straight \: line) \\ \\$ To find b, first we have to find angle FEG in ∆FEG Apply angle sum property of triangle $\angle \: FEG +\angle \: EFG +\angle \: FGE = 180° \\ \\ \angle \: FEG + 90° + 32° = 180° \\ \\ \angle \: FEG = 180° - 122° \\ \\ \angle \: FEG = 58° \\ \\$ Put this value to eq1 $25° +58° + \angle \: b = 180° \\ \\ \angle \: b = 180° - 83° \\ \\ \angle \: b = 97° \\ \\$ Thus, a°= 25 b°= 97° Hope it helps you. To learn more from brainly: 1)The figure SHOWS a rectangle ABCD. E lies on AB such that ADE= 51 and DCE = 68 brainly.in/question/21010222 2)brainly.in/question/20973554

given that ABC and BED are straight lines,find the values of the unknowns in each of the following figures

Answer»

Step-by-step EXPLANATION:

GIVEN: Given that ABC and BED are straight lines,FIND the values of the unknowns.

To find:a° and b°

Solution:

ABC is straight line.

$\angle \: ABE + \angle \: EBC = 180° \\ \\ \angle \: EBC = 180° - 115° \\ \\ \angle \: EBC = 65° \\ \\$

To find: a°

In ∆BCE, since angle BCE= 90°

apply angle SUM property of triangle

$\angle \: EBC + \angle \: BCE + \angle \: a = 180° \\ \\ 65° + 90° + \angle \: a = 180° \\ \\ \angle \: a = 180° - 155° \\ \\ \angle \: a = 25° \\ \\$

To find b°:

Since BED is a straight line

$\angle \: a + \angle \: FEG + \angle \: b = 180° \: \: \: ...eq1 \\ \\ (angles \: on \: straight \: line) \\ \\$

To find b, first we have to find angle FEG in ∆FEG

Apply angle sum property of triangle

$\angle \: FEG +\angle \: EFG +\angle \: FGE = 180° \\ \\ \angle \: FEG + 90° + 32° = 180° \\ \\ \angle \: FEG = 180° - 122° \\ \\ \angle \: FEG = 58° \\ \\$

Put this value to eq1

$25° +58° + \angle \: b = 180° \\ \\ \angle \: b = 180° - 83° \\ \\ \angle \: b = 97° \\ \\$

Thus,

a°= 25

b°= 97°

Hope it helps you.

To learn more from brainly:

1)The figure SHOWS a rectangle ABCD. E lies on AB such that ADE= 51 and DCE = 68