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: 0 / 2 part 1 of 2 the larger angle measures

Explanation:

Step1: Define variables

Let one angle be $x$. Then the other 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: $x = 14$.

Step5: Find the larger angle

The larger angle is $3x + 34$. Substitute $x = 14$ into it: $3\times14+34=42 + 34=76$.

Answer:

$76$