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(-2x + 10)° A (-4x+12)°
B
D
C
AD is an angle bisector. Find x and m/DAB

User Mhdwrk
by
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1 Answer

3 votes

Therefore, x = 1° and ∠DAB = 4°.

Since ∠DAB is bisected by AD, we have ∠DAB = ∠BAD.

From the diagram, we can see that ∠A + ∠B + ∠C + ∠D = 180°.

Substituting ∠DAB = ∠BAD, we get 2∠DAB + ∠B + ∠C = 180°.

Since ∠A and ∠C are opposite angles, we know that ∠A = ∠C.

Substituting ∠A = ∠C, we get 2∠DAB + ∠B + ∠A = 180°.

Therefore, ∠A + ∠B + ∠DAB = 90°.

From the diagram, we can see that ∠DAB + ∠B + ∠BAD = 90°.

Substituting ∠DAB = ∠BAD, we get 2∠DAB + ∠B = 90°.

Therefore, ∠DAB = (90° - ∠B)/2.

Since we are given that AD is an angle bisector, we know that ∠DAB = ∠BAD.

Substituting ∠DAB = ∠BAD, we get (90° - ∠B)/2 = ∠BAD.

Therefore, ∠BAD = (90° - ∠B)/2.

From the diagram, we can see that ∠A + ∠BAD = 90°.

Substituting ∠BAD = (90° - ∠B)/2, we get ∠A + (90° - ∠B)/2 = 90°.

Therefore, ∠A = ∠B/2.

Now we can solve for x and ∠DAB.

From the diagram, we can see that ∠A = -2x + 10° and ∠B = -4x + 12°.

Substituting ∠A = ∠B/2, we get -2x + 10° = (-4x + 12°)/2.

Solving for x, we get x = 1°.

Substituting x = 1° into the expression for ∠DAB, we get ∠DAB = (-2(1°) + 10°)/2 = 4°.

User Subhasis Das
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