Question

solve for the value of t.

Explanation:

Step1: Set up the equation

Since the two angles are complementary (sum to $90^{\circ}$), we have $(t - 4)+(2t + 7)=90$.

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: Solve for $t$

Subtract 3 from both sides: $3t+3 - 3=90 - 3$, which gives $3t=87$. Then divide both sides by 3: $t=\frac{87}{3}=29$.

Answer:

$t = 29$