Question

Circle F is congruent to circle J, and ZEFD = ZGJH.
m ZDFE = 80'. What is the measure of H?

Answer 1

50 deg

Explanation:

The circles are congruent, so all radii of both circles are congruent.

The given central angles are congruent, so the triangles are congruent by SAS.

Since each triangle has 2 congruent sides (the radii), opposite angles are congruent.

m<DFE = m<J = 80 deg

m<H = m<G = x

m<H + m<G + m<J = 180

x + x + 80 = 180

2x + 80 = 180

2x = 100

x = 50

m<H = 50

Answer 2

`m\angle H=50^(\circ)`

Explanation:

We are given that circle F is congruent to circle J.

`\triangle EFD\cong \triangle GJH`

`m\angle DFE=80^(\circ)`

We have to find the measure of H.

`m\angle DFE\cong m\angle GJH`

when two triangles are congruent then their corresponding angles and corresponding sides are congruent.

`m\angle DFE=m\angle GJH=80^(\circ)`

`m\angle JHG=m\angle JGH`

JH and JG are radius of circle J. Angles made by two equal sides are equal.

In
`\triangle GJH`

Let
`m\angle JHG=x=m\angle JGH`

`m\angle GJH+m\angle JHG+m\angle JGH=180^(\circ)`

By triangle angles sum property

Substitute the values then we get

`x+x+80=180`

`2x=180-80=100`

`x=(100)/(2)=50^(\circ)`

Therefore,
`m\angle JHG=m\angle H=50^(\circ)`