Question

Use the image below to answer the following parts.

Three adjacent angles where the angles are represented as expressions.

Part A: What is the relationship between the angles shown? Explain.

Part B: What is the value of x? Show all work.

Part C: What is the measure of ∠ABD,∠DBK,∠KBC and ? Show all work.

Answer 1

Explanation:

Part A

Since, the given angles are formed at a point are on a straight line, sum of these angles will be 180°.

Part B

(3x - 5)° + (4x + 2)° + (2x + 3)° = 180°

9x = 180

x = 20

Part C

m∠ADB = (3x - 5)°

= (3×20 - 5)°

= 55°

m∠DBK = (4x + 2)°

= (4×20 + 2)°

= 82°

m∠KBC = (2x + 3)°

= (2×20 + 3)°

= 43°