Question

solve for the value of t.

Explanation:

Step1: Note angle - sum property

The two angles are complementary (since they form a right - angle), so their sum is 90 degrees. We can write the equation $(t - 4)+(2t + 7)=90$.

Step2: Simplify the left - hand side

Combine like terms: $t-4 + 2t+7=(t + 2t)+(-4 + 7)=3t + 3$. So the equation becomes $3t+3 = 90$.

Step3: Isolate the term with $t$

Subtract 3 from both sides of the equation: $3t+3-3=90 - 3$, which simplifies to $3t=87$.

Step4: Solve for $t$

Divide both sides of the equation by 3: $\frac{3t}{3}=\frac{87}{3}$, so $t = 29$.

Answer:

$t = 29$