The value of x is 10° and the measure of angle DBC (m∠DBC ) is 60°
From the given information
We have that ∠ABD is complementary with ∠DBC
(NOTE: Complementary angles sum up to 90°)
That is,
∠ABD + ∠DBC = 90°
Also,
∠ABD = 2x+10 and ∠DBC = 10x-40
∴ 2x + 10 + 10x - 40 = 90°
a)
Now, solve for x
2x + 10 + 10x - 40 = 90°
This becomes
12x -30 = 90°
12x = 90° + 30
12x = 120
∴ x = 120 ÷ 12
x = 10°
b) To find m∠DBC
∠DBC = 10x - 40
Substitute the value of x
That is,
∴ m∠DBC = 10(10) - 40
m∠DBC = 100 - 40
m∠DBC = 60°
Hence, the value of x is 10° and the measure of angle DBC (m∠DBC ) is 60°
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