Question

select the correct answer. in the figure, angle k measures 45°. what is the measurement of angle c? a. 38° b. 45° c. 90° d. 98°

Explanation:

Step1: Identify vertical - angles

Angle K and the angle at vertex A (not labeled but vertical to K) are vertical angles. Vertical angles are equal, so the angle at A is 45°.

Step2: Use right - triangle property

In right - triangle ABC (angle A = 45°, angle BAC = 90°), we know that the sum of the interior angles of a triangle is 180°. Let angle C be \(x\). Then \(45^{\circ}+90^{\circ}+x = 180^{\circ}\).

Step3: Solve for angle C

\[

$$\begin{align*} x&=180^{\circ}-(45^{\circ} + 90^{\circ})\\ x&=180^{\circ}-135^{\circ}\\ x& = 45^{\circ} \end{align*}$$

\]

Answer:

B. 45°