Question

Angle DEB is 42. State the size of angle ABD

Answer 1

The answer would be 80 ° because 5×( 2 + 13 or x +1 ) is 80

Step-by-step explanation:

ABD is 80°

If DEB is 42 °

∠ ABD = 5(2X+1)

∠ DBC = 3X+6

∠ EBC = Y +135/2

∠ ABD and ∠ DBC are linear pairs

∴ ∠ ABD +∠ DBC = 180

∴ 5(2X+1) + 3X+6 =180

solve for x

∴ x = 13

∴∠ ABD = 5(2X+1) = 5(2*13+1) = 135

∠ DBC = 3x+6 = 3*13+6 = 45

∠ ABD and ∠ EBC are vertical angles

∴ ∠ ABD = ∠ EBC = 135

∴ y +135/2 = 135

∴ y = 135/2

Answer 2

The measure of angle ABD is determined as 84⁰.

How to calculate the measure of angle ABD?

The measure of angle ABD is calculated by applying the following formula as follows;

The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

So the value of arc angle AD is calculated as;

arc AD = 2 x m ∠ BED (circumference angle of intersecting chords)

arc AD = 2 x (42)

arc AD = 84

The value of angle ABD is calculated as;

m∠ABD = arc AD (tangent angle of intersecting chords)

m∠ABD = 84

Thus, the measure of angle ABD is 84⁰.