Question

solve the application involving geometry. if necessary, refer to the geometry formulas listed in the inside back cover of the text. two angles are complementary. one angle measures 34° more than 3 times the measure of the other. what are the measures of the two angles? part 1 of 2 the larger angle measures 76°. part: 1 / 2 part 2 of 2 the smaller angle measures

Explanation:

Step1: Define variables

Let the smaller angle be $x$. Then the larger angle is $3x + 34$.

Step2: Use complementary - angle property

Since the two angles are complementary, their sum is $90^{\circ}$. So, $x+(3x + 34)=90$.

Step3: Simplify the equation

Combine like - terms: $4x+34 = 90$.

Step4: Solve for $x$

Subtract 34 from both sides: $4x=90 - 34=56$. Then divide both sides by 4: $x = 14$.

Answer:

14