Question

use the image below to find the requested values.
find the measure of ∠kpd.
what is the value of t?

Explanation:

Step1: Use the property of right - angle

Since \(\angle KPB = 90^{\circ}\), and \(\angle KPB=\angle KPD+\angle DPB\), where \(\angle DPB = 30^{\circ}\).
By the angle - addition formula \(\angle KPD=90^{\circ}-\angle DPB\).
Substitute \(\angle DPB = 30^{\circ}\) into the formula: \(\angle KPD=90 - 30=60^{\circ}\).

Step2: Solve for \(t\)

We know that \(\angle KPD=(t - 25)^{\circ}\), and we found \(\angle KPD = 60^{\circ}\).
Set up the equation \(t-25=60\).
Add \(25\) to both sides of the equation: \(t=60 + 25\).
So \(t = 85\).

Answer:

The measure of \(\angle KPD\) is \(60^{\circ}\), and the value of \(t\) is \(85\).