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## Question:

unit 10: circles Homework 4: Inscribed angles. please complete the following questions and explain how it is done.

## Answer:

5) The **sum** of angle in the **triangle DEF** is **180 degrees**

mFE = <D

Recall that <D+<E+<F = 180⁰

<D+63+90 = 180

<D = 180-153

<D = **27 degrees**

Hence the measure of **arc FE** is **27degrees**

6) For this circle geometry, we will use the theorem

The **sum** of **Opposite side of** a cyclic **quadrilateral** is **180 degrees**.

A + C = 180

m<A + 101 = 180

m<A = 180-101

m**<A = 79degrees**

Similarly

B + D = 180

m<B + 68 = 180

m<B = 180-68

**m<B = 112degrees**

7) The sum of angle in a circle is 360, hence;

arcGJ+68+31+115 = 36p

arcGJ = 360 – 214

arcGJ = 146⁰

Since the **angle** at the **centre** is **twice** angle at the **circumference**, then;

<GHJ = 1/2 arcGJ

<GHJ = 1/2(146)

<GHJ = 73⁰

**<GHJ = <GIJ = 73⁰** (**angle** in the **same segment** of the circle are **equal**)

8) Recall that the **sum** of **Opposite side of a** cyclic **quadrilateral** is **180 degrees**.

P + R = 180

57 + <R = 180

m<R = 180-57

m**<R = 123degree**s

Similarly, m<Q+m<S = 180⁰

Since the **triangle** in a **semi circle** is a **right angled** triangle, hence m<Q = 90 degrees (triangle PQR is a right angled triangle)

m<S = 180 – 90

**m<S = 90 degrees **

**Learn**** ****more**** ****here****:**** ****brainly.com****/****questions****/****113255****4**

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