Question

find the measure of angle a
22)
find the measure of angle a
24)

Explanation:

Problem 22

Step1: Sum of angles in right triangle

$(x+37)+(x+67)+90=180$

Step2: Simplify equation

$2x + 194 = 180$ → $2x = -14$ → $x=-7$

Step3: Calculate angle A

$(-7)+37=30$

Step1: Exterior angle equals sum of remote interior angles

$4x+17=(x+23)+80$

Step2: Simplify equation

$4x+17=x+103$ → $3x=86$ → $x=\frac{86}{3}$ (Note: Assuming possible typo, if exterior angle is correct, proceed)

Step3: Calculate angle A

$\frac{86}{3}+23=\frac{86+69}{3}=\frac{155}{3}\approx51.67$ (If typo corrected to exterior angle $4x-17$, then $4x-17=x+103$ → $3x=120$ → $x=40$, angle A=63)

Answer:

30

Problem 24