Question

3. Given that ∠ABD is complementary with ∠DBC, ∠ABD = 2x+10 and ∠DBC = 10x-40:

Answer 1

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°

Learn more here: brainly.com/question/18277030