Question

for each part below, use the figure to fill in the blank. if necessary, you may learn what the markings on a figure indicate. (a) find ( mangle x ). ( mangle x = square^circ ) (b) find ( mangle v ). ( mangle v = square^circ )

Explanation:

Part (a)

Step1: Identify triangle type

Triangle \( WYX \) has \( XY = XW \) (marked equal), so it's isosceles with \( \angle Y=\angle W = 35^\circ \).

Step2: Sum of angles in triangle

Sum of angles in a triangle is \( 180^\circ \). Let \( m\angle X = x \). Then \( 35^\circ + 35^\circ + x = 180^\circ \).

Step3: Solve for \( x \)

\( 70^\circ + x = 180^\circ \), so \( x = 180^\circ - 70^\circ = 110^\circ \).

Step1: Identify triangle type

Triangle \( UTV \) has \( UT = TV = VU = 11 \), so it's equilateral.

Step2: Angles in equilateral triangle

All angles in an equilateral triangle are \( 60^\circ \), so \( m\angle V = 60^\circ \).

Answer:

\( 110 \)

Part (b)