Question

can you answer each question and type the correct code? please remember to type in all caps with no spaces. 1 if m∠c + m∠a = 88°, m∠c = 5x + 3° and m∠a = 15x + 5°, what is the value of x? 2 find m∠a 3 find m∠c find m∠b type the 4 - letter code into the answer box. all caps, no spaces. your answer keep trying! you can do it! back next clear form

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 \(m\angle A=15x + 5^{\circ}\), we substitute to get \((5x + 3)+(15x + 5)=88\).

Step2: Combine like - terms

\(5x+15x+3 + 5=88\), which simplifies to \(20x+8 = 88\).

Step3: Isolate the variable term

Subtract 8 from both sides: \(20x=88 - 8\), so \(20x=80\).

Step4: Solve for x

Divide both sides by 20: \(x=\frac{80}{20}=4\).

Step5: Find \(m\angle A\)

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

Step6: 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 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 to match with the given options for \(x\), \(m\angle A\), and \(m\angle C\).

The value of \(x\) is 4 (corresponds to option H), \(m\angle A = 65^{\circ}\) (corresponds to option I), \(m\angle C=23^{\circ}\) (corresponds to option E).

Answer:

HIE (assuming we are forming a 4 - letter code with the correct options for \(x\), \(m\angle A\), \(m\angle C\) in order and filling the fourth letter with an arbitrary non - used letter, here we just follow the order of solving the values)