Question

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

Answer 1

Answer:

50 deg

Step-by-step 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

Answer:

$m\angle H=50^{\circ}$

Step-by-step 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

$x+x+80=180$

$2x=180-80=100$

$x=\frac{100}{2}=50^{\circ}$

Therefore, $m\angle JHG=m\angle H=50^{\circ}$