Question

n trapezoid STUV, SW is an altitude. Which is equivalent to the measure of angle m + n + p if m angle VSW = 65 degrees?

Answer 1

4th Option is correct.

Explanation:

Given: STUV ia a trapezoid that is ST is parallel to UV

SW is altitude that is m∠ SWV = 90°

m∠ VSW = 65°

To find: measure of m + n + p

Since, ST is parallel to UV.

⇒ n + p = 180° because Sum of Interior Angle on the same side of traversal is 180°

Now, In ΔSVW

∠SVW + ∠SWV + ∠WSV = 180° (Angle sum property of triangle)

m + 90° + 65° = 180°

m + 155 = 180

m = 180 - 155

m = 25°

Thus, m + n + p = 25 + 180 = 205°

Therefore, 4th Option is correct.

Answer 2

The measure of angle m+n+p is equivalent to 205° (Fourth option)

Explanation:

In a quadrilateral, the sum of the interior angles must be equal to 360°:

S=m+n+p+m<VSW+m<WST=360°

m<VSW=65°

Like SW is an altitude, m<WST=90°

Replacing the known values in the formula above:

m+n+p+65°+90°=360°

Adding like terms:

m+n+p+155°=360°

We want m+n+p, then subtracting 155° both sides of the equation:

m+n+p+155°-155°=360°-155°

m+n+p=205°