Question

puzzle #4
1 if m∠c + m∠a = 88°, m∠c = 5x + 3° and m∠a = 15x + 5°, what is the value of x?
answer choices
a: 28 b: 5 c: 62
d: 45 e: 23 f: 8
g: 88 h: 4 i: 65
2 find m∠a
3 find m∠c
4 find m∠b
type the 4 - letter code into the answer box. all caps, no spaces.

Explanation:

Step1: Substitute angle - expressions into the sum - equation

Given \(m\angle C + m\angle A=88^{\circ}\), \(m\angle C = 5x + 3^{\circ}\), and \(m\angle A=15x + 5^{\circ}\). Substitute these into the equation: \((5x + 3)+(15x + 5)=88\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \(5x+15x+3 + 5=88\), which simplifies to \(20x+8 = 88\).

Step3: Solve for \(x\)

Subtract 8 from both sides of the equation: \(20x=88 - 8=80\). Then divide both sides by 20: \(x=\frac{80}{20}=4\).

Step4: Find \(m\angle A\)

Substitute \(x = 4\) into the expression for \(m\angle A\): \(m\angle A=15x + 5=15\times4+5=60 + 5=65^{\circ}\).

Step5: Find \(m\angle C\)

Substitute \(x = 4\) into the expression for \(m\angle C\): \(m\angle C=5x + 3=5\times4+3=20 + 3=23^{\circ}\).
Assuming this is a triangle and the sum of angles in a triangle is \(180^{\circ}\), \(m\angle B=180-(m\angle A + m\angle C)=180-(65 + 23)=92^{\circ}\), but we only need the values corresponding to the answer - choices for the code.
The value of \(x\) is 4 (choice H), \(m\angle A = 65^{\circ}\) (choice I), \(m\angle C=23^{\circ}\) (choice E).

Answer:

HIEI