Question

7 mark for review
in triangle abc, the measure of angle a is 54°, the measure of angle b is 90°, and the measure of angle c is (k/2)°. what is the value of k?
a 36
b 45
c 72
d 108

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \( \angle A + \angle B + \angle C = 180^\circ \).

Step2: Substitute known angles

We know \( \angle A = 54^\circ \), \( \angle B = 90^\circ \), and \( \angle C = \frac{k}{2}^\circ \). Substitute these into the formula: \( 54 + 90 + \frac{k}{2} = 180 \).

Step3: Simplify and solve for k

First, add \( 54 \) and \( 90 \): \( 144 + \frac{k}{2} = 180 \). Then, subtract \( 144 \) from both sides: \( \frac{k}{2} = 180 - 144 = 36 \). Multiply both sides by \( 2 \): \( k = 36 \times 2 = 72 \)? Wait, no—wait, wait, let's check again. Wait, \( 180 - 54 - 90 = 36 \), so \( \frac{k}{2} = 36 \), so \( k = 72 \)? Wait, no, wait the options: C is 72. Wait, but let's recalculate. \( 54 + 90 = 144 \). \( 180 - 144 = 36 \). So \( \frac{k}{2} = 36 \), so \( k = 72 \). Yes, that's correct.

Answer:

C. 72