Question

Question
Quadrilateral QUAD
is inscribed in circle O
. The m∠U=65°
and mDQU=170°
. Use the properties of inscribed quadrilaterals to determine m∠Q
.(1 point)
Responses

95°
95°

85°
85°

115°
115°

130°
130°

Answer 1

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary. This means that the sum of the measures of opposite angles equals \(180^\circ\).

Given:
- \( m\angle U = 65^\circ \)
- \( m\angle DQU = 170^\circ \) (which we interpret as \( m\angle Q = 170^\circ \))

To find \( m\angle Q \) (which is actually \( m\angle UQD \)), we can use the rule for cyclic quadrilaterals:

1. Use the property of supplementary angles:
\[
m\angle U + m\angle Q = 180^\circ
\]

Substituting in the value of \( m\angle U \):
\[
65^\circ + m\angle Q = 180^\circ
\]

2. Solve for \( m\angle Q \):
\[
m\angle Q = 180^\circ - 65^\circ = 115^\circ
\]

Thus, the measure of \( m\angle Q \) is \( 115^\circ \).

**The correct answer is: 115°**.