Question

∠ADC and ∠CDJ are complementary angles. What is the m∠ADC?

*Hint, first find the value of x, then find the measure of the angle.

Line A K and line M J intersect at a right angle at point D. Line L C also passes through point D, forming angle A D C and angle J D C. Angle A D C measures four x degrees, and angle J D C measures three x minus eight degrees.


Question 6 options:

90°


56°


14°


34°

Answer 1

∠CDJ = 34°.

Explanation:

In this question AK and MJ intersect at 90°.

∠ADC = 4x° and ∠JDC = (3x - 8)°

We have to find the measurement of ∠CDJ.

Since ∠MDA = ∠KDJ = ∠ADJ = ∠MDK = 90°

Therefore ∠ADJ = ∠ADC + ∠JDC = 90°

4x + 3x - 8 = 90

7x - 8 = 90

7x = 98

x = 98/7 = 14

Therefore m∠CDJ = 3x - 8 = 3×14 - 8 = 42 - 8 = 34°

Answer is m∠CDJ = 34°